Kinematic design of linkage-based haptic interfaces for medical applications: a review

Touch is the first sense that humans develop. Tactile and kinesthetic perceptions are used to understand objects' various properties, such as shape and stiffness, through the skin and muscle stimulation [1]. This combination of perceptions, known as haptic perception, provides humans with their most basic method of understanding and effecting change over an environment. A related concept, haptic feedback, can stimulate this perception for humans who operate machines to interact remotely with an environment, allowing for safe, reliable, and precise interaction [2].

To emulate touch, a haptic interface produces forces matching sensed force data received from the robotic or virtual (follower) proxy probe. A haptic teleoperation system or virtual environment (depending on whether the proxy is robotic or virtual) is created for the user to interface with the proxy to interact with the remote environment. The applied haptic feedback of the proxy's interaction with the environment gives transparent (that is, a real-feeling, high fidelity) touch stimulation to the user to emulate actual direct interaction with the environment by the user more accurately. Such systems have found use in domains that include medicine—for surgical training by use of a virtual proxy, in robotic (tele-)surgery, and in (tele-)rehabilitation via a virtual or robot proxy, as examples [2].

A haptic interface is therefore an actuated, computer-controlled, and instrumented machine that establishes a bilateral interaction between the virtual or remote environment and the operator. The property of being not just an interface for input but also a source of user feedback makes haptic feedback devices unique, and the quality of their hardware and the design of their controllers will directly alter the realism, presence, and immersion of the user in the virtual or remote environment, and therefore their ability to control the proxy's environment [3].

Giving force information to the user is meant to improve the telemanipulation experience to make the user feel as if they are themselves present in a remote environment [4]. This is often called the transparency of an interface [5]. Haptic interfaces do not stop with this; they attempt to create the illusion of telepresence by allowing users to interact with operative information via force constraints that have been generated virtually [6]. Active constraints, also called virtual fixtures [7], are software-generated force responses to user movements that are meant to encourage motion within a particular range, away from forbidden areas and/or along determined paths, allowing robotic precision to be used while leaving the human operator in control of motion occurrence and timing [4]. Haptic interfaces can also make a record of the intentions of the user along the interaction path, use this data to invoke visualization systems or preset user commands that may result in direct haptic feedback [8].

Haptic interaction began its current rate of growth in the 1990s. The cost of components has decreased over time, so new designs and differently sized haptic interfaces have become available [2]. Specialized hardware often needs to be invented or modified from other machinery in order to create haptic devices, but most haptic interface designers have not been engineers, so many haptic innovations have been spread in a fragmented literature [9].

Haptic interfaces are used for a variety of tasks. Many haptic feedback systems are used for training surgeons without risking a patient's health [10–12], also generally giving visual and acoustic feedback to emulate a procedure realistically. In the same way that a flight simulator works for pilot training, virtual operating rooms can be used for surgeon training while guaranteeing quantitative feedback so that the trainee can refine their practice before exercising the skills gained on actual patients [13, 14]. Other systems train joint lesion diagnosis or simulate endoscopies, laparoscopic, and intravascular interventions [3]. Better task performance has been shown by simulator-trained surgeons than those without such training [15, 16]. Given that patients are not placed in jeopardy in these simulations, early student training can be accomplished using these devices with better overall results [8]. Haptic devices have additionally been used for augmenting graphical user interfaces [17], scientific data visualization [18], enhancement of nano-manipulation systems [19], CAD/CAM [20], education and training, particularly surgical training [21], master interfaces in teleoperation [22], master interface in surgery [2, 23–25], and rehabilitation [26–28]. It has been nearly thirty years since the first attempts were made to add robots to operating rooms [29]. Though still controversial [30, 31], in particular as relates to their cost-benefit value [13, 14], robotic systems are added each year to operating rooms in the interest of more positive surgical results [13, 14], which arguably are highly dependent on the interface connecting the surgeon to the surgical robotic system. This fact highlights the importance of the design of haptic devices in such systems.

Different haptic devices provide sensations in different fashions. Hence, a variety of mechanical, electrical, and computational elements are needed to fulfill varying design specifications for different applications, such as surgery, education, and games, where producing useful haptic interfaces involves incorporating ideas, hardware, and interactions among experts and professionals from different areas. This incorporation has become essential considering the widespread use of virtual reality and physical computing to, for instance, digitally simulate/recreate physical objects in order to sense and respond to the world around interactive systems [9]. Thus, the design of a haptic device is crucial to its intended application. The problem left unsolved here is that the knowledge of haptic device design developed in the last decades has not been consolidated for the benefit of contemporary designers because this information has been fragmented in the areas of haptics, robotics, virtual reality, and human-computer interaction [9]. As a result, the need for a review paper on this area arises.

The contribution of this paper is filling the stated gap of research in the design of haptic interfaces by addressing the main categories of the mechanical design of haptic devices and introducing the contributing factors in each of the design classes as well as highlighting the criteria for evaluating the merits of a haptic interface from the design perspective. Moreover, a comparison table will provide the readers with a report on the most common haptic interfaces designed to date, together with some of their specifications.

The scope of this paper is demonstrated in figure 1. The taxonomy of haptic interfaces can be introduced from different perspectives. This review focuses mainly on the kinematic design of linkage-based haptic interfaces. However, we briefly introduce non-linkage-based haptic devices as well to draw the attention of researchers to these fast-paced, ever-growing haptic technologies in the community. There are still other haptic devices excluded from the review due to limited space, the main scope of the review (i.e. mechanical design perspective), and review distinctions.

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The structure of the paper is as follows. Section 2 opens up the avenue to the applications of haptic devices in medical areas. Section 3 states the most important design considerations of linkage-based haptic interfaces. The desired characteristics of such haptic interfaces are then discussed in section 4. Section 5 investigates the advantages, challenges, and limitations of the main types of kinematic chains in the structure of linkage-based haptic interfaces. An overview of the methods of performance evaluation for the designed interfaces is presented in section 6. Some future design perspectives of linkage-based haptic devices and the potentials of the redundant haptic interfaces are discussed in section 7. Non-linkage-based haptic interfaces have also merits that are briefly introduced in section 8. The design requirements in medical fields are shortly stated in section 9. Section 10 provides information on the current challenges and promising future directions. Despite all technological advancements in haptic technologies, there are still challenges and promising future directions especially in medical applications which are discussed in section 10. Section 11 finally concludes the paper.

One important application of haptic devices is in the design and development of surgical simulators for operations like stitching, palpation, dental procedures, endoscopy, laparoscopy, and orthopedics [32]. For example, a surgical simulator for training, called SatureHap, was designed and developed using Phantom Omni or Touch haptic device [33]. A popular medical simulation system was discussed for the dental training system, as well as the development of an oral implantation simulator that can store data collected from trainees and to be potentially used for rehearsal and medical education [33]. Haptics technology has a growing importance in surgical operations, especially minimally invasive surgery (MIS) that is commonly used in conjunction with a robotic manipulator in a bilateral teleoperation surgical system [34, 35]. In some systems, an industrial robotic arm was used in a teleoperation system for MIS that was a modified six-degrees-of-freedom (6-DOFs) Denso VP-6242G with a serial mechanism and a PHANToM Premium 1.0 kinesthetic haptic device. In this system, the serial manipulator was employed as the follower, and the haptic device as the master [36]. An adjustable, immersive, and configurable platform for optometry training simulation was proposed, involving head-mounted displays, augmented reality interfaces, and a multi-point haptic device [37]. In another platform, preoperative planning and virtual training system were developed based on force feedback. The platform involved an Omega 6 haptic device, an immersive workstation, and a CHAI3D software toolkit (a software toolkit based on C++ for haptic simulation). Using this system, the preoperative planning data are transferred, and surgical simulations are carried out by a novice surgeon for osteotomy procedures to learn and improve their surgical skills [38]. The construction of pneumatic artificial muscles (PAMs) was proposed in [39]. These PAMs have flexible and inflatable membranes, exhibiting orthotropic material behavior. Being light and formed conveniently, PAMs are also of interest for rehabilitation purposes due to their functionalities as locomotion devices [39]. The importance of haptic force feedback was shown in identifying the interaction force between the surgical instrument and human organ and tissue in virtual surgery [40]. Navigation in surgery was possible with the help of tactile and force feedback between the surgical instrument and the human organ [40]. An application of Omega 7 haptic devices is in the second generation of neuroArm surgical system that uses two haptic devices to transfer the sense of touch to both hands of a surgeon. A haptic intracorporeal palpation was proposed that uses a cable-driven robotic system and includes a remote sensing strategy [41]. The platform employs teleoperated cable-driven parallel manipulator that is a new, simple, and cost-effective approach for restoring haptic sensation during the performance of intracorporeal palpation. The conducted tests showed evidence of reasonable accuracy in estimating the amount of force. In another work, the authors integrated a 7-DOF master device into the da Vinci Research Kit and conducted tissue grasping, palpation, and incision tasks using robot-assisted surgery by experienced surgeons, surgical residents, and non-surgeons [42]. Statistical analysis showed that haptic feedback improves key surgical outcomes for tasks requiring a pronounced cognitive burden for the surgeon; however, possible longer task completion times were observed. Nevertheless, these are just some examples of the usage of haptic devices in medical applications, not a comprehensive survey.

One of the highly important design considerations of haptic interfaces is the structural transparency, with the back-drivability of the system such that the user perceives only the mechanical impedance being represented or reflected rather than that of the device's structure. Therefore, all of the mass, inertia, backlash, and friction must be reduced when possible. Additional issues such as workspace and payload capacity are usually important as well, but not so much as those mentioned above. In the same way, the fidelity of force feedback is more important than positional accuracy. Moreover, some particular designs make the kinematics uncomplicated and the dynamics decoupled or nearly decoupled, which are very useful simplifications of the system for control purposes [43].

The advantages of an effective design, however, are many. For instance, it enables the perception of extremity movement and position, improves the skilled performance of tasks by typically increasing the precision and speed of execution, and allows for a safe and repeatable virtual training [28]. When dealing with teleoperation, force feedback can reduce completion time, decrease peak forces and torques, and decrease cumulative forces and torques [44–47]. These achievements are particularly useful in training because the related virtual environments can set up a context for developing a safe and repeatable practice where the intimation of realism is improved, making the transfer of skills from the virtual into reality more likely. Besides, the performance of hand-eye coordination tasks and specifically dexterous manipulations can be improved by haptic interfaces [28]. As a tool, it can warn people about critical tasks in an effective way, make a spatial frame of reference available for the user, and improve the performance of tasks that entail hand-eye coordination [28, 48]. All these capabilities make haptic feedback systems a worthwhile area of study, and hence a conceptual design space well in need of mapping through surveys such as this one.

It is useful to evaluate a haptic interface through quantitative and qualitative measures of realistic rendering, performance, and enhancement, where the performance can be thought of as a measure of how capable the interface is in rendering a large spectrum of haptic stimuli [3, 49]. In order to evaluate the quality of a haptic feedback device in connection with force and torque feedback, the preliminary requirements have been utilized to derive a group of performance indices [50–53], but requirements for performance are usually multiple and indeed at times coupled or conflicting, such as possessing large stiffness and small inertia, having low weight and large enough workspace, and incurring low cost while having high functional performance. Some performance indices based on the stated requirements are often considered as objective functions of optimization subroutines that are sought to be minimized or maximized. Many attempts have been made to date to find an optimal haptic feedback device in this way, but predicting performance normally requires analyzing and simulating heterogeneous and complex models that are computationally intensive and demands design prototyping before guaranteeing the performance [53].

The usual method for determining the most fundamental and mechanical properties of a haptic interface involves ascertaining their desired characteristics. Various researchers have listed and categorized the most important requirements for proper performance [3, 52, 54, 55]. No specific values, in general, have been discovered, as the properties required are usually specific to the targeted device application. However, there is an agreement among experts of the area on the desired characteristics in each application [52, 53, 56–58]. The general design criteria are as follows. Table 1 then summarizes the highlights of these criteria.

• Workspace: The workspace may indeed be the most important manipulator property in that workspaces have inherent requirements given by the specifications of the user's task. The number of DOFs, the configuration of the kinematic chain, and the shape and volume of the workspace are all very important for task execution. The freedom of movement of a manipulator defines the workspace for user task achievement, and in the case of a haptic interface, the workspace should be large enough to equate with the real space required for task success by the human arm and the attached follower device. As regard the largeness of the haptic device workspace, it should match a comfortable range for the user. A large workspace that is cumbersome or fatiguing for the user does not add to the merits of the device. For instance, small motions of a computer mouse are mapped easily to the motions of a large pointer across a large monitor. But it is harder to match the scale of the mouse motion to the displayed pointer motion. The desirable workspace size is therefore application-dependent. Keeping that in mind, if the workspace is not large enough, users might be forced to work in a much slower fashion and use clutching to move the haptic interface repeatedly to a new position and orientation (pose) without moving the follower device [53]. The accuracy of the majority of MIS systems in real surgical operations has been improved by scaling down the motion of the follower side rather than that of the master side. While the shape of the workspace is maintained, the motion scaling extends the workspace volume required for the master side by increasing the length of each link proportional to the scaling factor.
• Dexterity: The dexterity or manipulability of the interface is a measure of its capacity to apply any arbitrary force and torque and to find any arbitrary pose within the given workspace [59]. An attached important factor is the interface's isotropy, providing to what extent a haptic interface might be uniform in its motion and force production in varying directions, which full isotropy is known as directional uniformity [53].
• Stiffness and maximum force feedback: By producing large forces against the user, even despite limited joint torque, a haptic interface should emulate environments of high stiffness, else the real environment will be translated to the user in a way that they read as softer than in reality [53].
• Light weight, low friction, and back-drivability: If the follower moves within free space, the interface itself should exert no wrench on the user's hand(s), and therefore requires low impedance (mainly inertia) and low friction. In particular, this is important with high accelerational motions. The mechanical structure, configuration, and actuators of the interface will define its frictional and inertial qualities. An impedance, being the ratio of force out to motion input, contains inertia, damping, and stiffness components [53].
• Fast response (large bandwidth): Bandwidth determines the speed and frequency at which the interface may operate at maximum. This is the bandwidth of actuation for force generating capability of the haptic device. To create high enough resolution rendering of the transitions between stiff contact points and free space, as well as of various textures, the bandwidth range must be high. Interfaces are regularly designed to be lightweight, encouraging larger bandwidth [53].

The desirable qualities of an interface have large trade-offs, an example being between the maximum force feedback capability of an interface and its minimum inertia; otherwise, its workspace size traded off against the maximum stiffness it may depict. For a larger force feedback capability, large actuators must be used, which in turn increases haptic interface inertia. Large workspaces subsequently require longer links, which will decrease the interface's stiffness and increase its inertia. For this reason, haptic interfaces have to be optimized for their particular application(s) [53].

Designing the kinematics of a haptic interface is of high importance, particularly when designing for those interfaces that provide haptic feedback predominately—as with most robotic haptic feedback interfaces. In such devices, to link the user to the actuators of the device for providing the feedback, a machine or mechanical mechanism is used. Often, a joystick-like mechanism is used by the user to provide input commands. Consequently, to provide good haptic feedback within an ergonomic design, the most important characteristic of the device becomes the design of the kinematics [8].

In the analysis of the mechanisms and machines, the base link (link number 0) is that section of the mechanism that is considered stationary. The motion of all other links and joints of the mechanism, in terms of the position, velocity, and acceleration, are all calculated with respect to the base link. In most mechanisms, the base link is connected to the rest of the mechanism with at least one joint or kinematic pair. The rest of the kinematic pairs and links form a kinematic chain connecting the base link to the end-effector of the mechanism. The most commonly used kinematic pairs are prismatic (P), revolute (R), helical (H), universal (U), spherical (S), and cylindrical (C) joints. The mechanism interacts with the task environment at its end-effector, which is usually capable of moving in the 3D space with a defined number of DOFs with respect to the base link (base frame). If the base link is located on a mobile platform, it adds extra DOFs to the system, which are usually considered separately for motion analysis to make the mathematical equation manageable. The end-effector of a haptic device is usually the point where interaction between the operator and the device takes place [8].

One way to classify mechanisms is based on the design of their kinematic chain that can be an open kinematic chain (or serial design), a closed kinematic chain (or parallel design in which there should be at least two distinct kinematic paths from the base link to the end-effector), or a combination of open and closed kinematic chains, which is called a hybrid design (a mixture of serial and parallel designs). Depending on the application, one of the suitable designs mentioned above is used for the haptic interface [60, 61]. Figure 2 depicts different structures of the haptic interfaces.

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The type of kinematic pairs and actuators used in the design of a haptic device are very important aspects of the type synthesis. Revolute joints and rotary actuators usually impose less friction and have superior back-drivability than prismatic joints and linear actuators. Therefore, they are most commonly used in commercially available haptic devices [61].

While being used, the haptic device and the human operator are mechanically coupled. As a result, it is very important to match the characteristics of these two systems, such as the size of the workspace and positional bandwidth, the magnitude of the force and force bandwidth, the velocity and acceleration, and the accuracy or the resolution of the systems [62]. This will ensure that the designed haptic interface provides a safe and effective interaction experience for the human operator that is not overqualified for the task at hand [28].

In the designing of a haptic interface, the first step is to choose the structural configuration of the system, including links, kinematic pairs, and actuators to be used in the device [8]. Depending on the application of a haptic interface or the body part with which it interacts, a suitable mechanism can be chosen. There are two types of mechanisms, serial and parallel, each of which has its own pros and cons. In serial mechanisms, a series of links are connected back-to-back, the first link is grounded, and the last link is the end-effector. This provides simplicity in design and control system; however, these mechanisms require larger motors for the same force capability. Moreover, error at the end-effector results from a combination of errors from all links and joints. In contrast, there are loops of kinematic chains in parallel mechanisms connected to the base (ground) link by two or more joints. While parallel mechanisms can provide high stiffness and precision with low inertia at the end-effector, they have a smaller workspace and are harder to control [28].

A number of haptic interfaces have been designed for a variety of applications in the last few years. These interfaces range from simple single-DOF devices [63] to complex and multi-DOF devices [64, 65]. Table 2 lists detailed specification of some of the most common haptic interfaces have been developed in the last three decades. More haptic devices can be seen in Haptipedia [9], a growing database of 105+ haptic devices have been invented since 1992. A high-DOF serial robot can have a larger workspace compared to a low-DOF robot of a similar size. The same point, however, does not remain necessarily valid for parallel robots. A haptic interface's mechanical design includes the robot's DOF determination, its kinematic mechanism, and the portability of the robot. A haptic interface's most prominent feature is the number and nature of DOFs at the active end(s), with the active end referring to the section of the robot interfacing directly with the operator's body. At this end, a hand usually holds the device, or the robot itself braces the user's body—if no such reciprocal interface exists, the interaction is considered unilateral [55]. Both active (actuated) and passive DOFs are critical to an interface's performance [28].

5.1. Design requirements

5.2. Haptic interfaces with serial mechanism

Serial mechanisms are commonly employed in a broad spectrum of robotic applications. In a solely serial mechanism, no passive joints are employed as the actuators are arranged in serial from the first to the last link of the kinematic chain. These mechanisms have several well-known advantages. For example, they are simple-to-design and fairly large-workspace mechanisms. Since the links and joints of these mechanisms are in a serial sequence, a step-by-step mathematical tool, such as the Denavit–Hartenberg algorithm, can be used to easily model and control the mechanism, particularly in positioning tasks. The main limitation of these mechanisms is their restricted dynamic behavior rooted in their fairly high mass. The high mass of the links is the consequence of the desire to have high structural stiffness. Moreover, the weight of the actuators that are expected to accelerate the following actuators of the chain adds to the mass of the mechanism. The structural stiffness with respect to the weight of serial mechanisms is also usually low because a single kinematic chain is expected to carry a load.

Given any limit in the accuracy of the joints of a serial mechanism imposed by cost or unavailability of component, the distal joints should sense the angular position more accurately than the proximal joints; similar to the distal joints of humans that have better joint angle resolution than the proximal joints [92]. However, Considering the general design criteria, the requirement of actuating remote joints in a haptic device that reflects force makes a serial mechanism less desired. In this case, most of the volume and mass of the joints come from the motors and gear reducers. Employing a cabled transmission to place actuators at the base of the mechanism is a solution, but the cable routing becomes more complex with each DOF.

PHANToM (3D Systems Inc., USA) is one of the haptic devices widely used all over the world [57, 93], which has been designed in different versions based on the application (see figure 3). 3D Systems Touch is a fairly low-price and highly popular one that possesses six-DOF position and orientation sensing as well as a workspace of $160\times120\times70\,\mathrm{mm}$. The maximum force feedback of the device in its three translational DOFs can reach 3.3 N. In the enhanced version of the device, called 3D Systems Touch X, the user has been provided with a larger workspace, higher resolution of positioning, and higher maximum force feedback ($7.9\,\mathrm{N}$). PHANToM Premium is also a haptic device family produced by 3D Systems Inc. in different models to meet the expectations of the users by a much larger workspace and higher resolution of positioning. These models can also render the force feedback in a better range compared to the previous versions. PHANToM Premium 1.0, 1.5, and 3.0 are the three main devices in the family. In addition, a 6-DOF version of the PHANToM Premium 1.5 and 3.0 (three force and three torque feedback) have been presented to the market by the producer. The workspace of the 6-DOF PHANToM Premium 3.0 is $838\times584\times406\,\mathrm{mm}$, and it can reach a maximum force and torque feedback of $22\,\mathrm{N}$ and $0.52\,\mathrm{Nm}$, respectively. Due to utilizing serial kinematic chains in the design, 3D Systems Inc. has succeeded in producing large-workspace haptic devices, but the force and torque feedback of these devices is inferior to that of haptic devices designed with parallel kinematic chains. Forsslund et al [94] designed an open-hardware Do it yourself (DIY) kit for novices to produce a spatial haptic interface equal to a PHANToM Desktop with some guidance and without specialized knowledge or tools, meant to be alterable by designers without the need for electromechanical expertise.

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Virtuose (Haption, Soulgé-sur-Ouette, France) is also a haptic device family with a serially-chained kinematic design that can sense the position with 6 DOFs [69–73] (see figure 4). There are two classes of 3D and 6D models in this family. The force feedback provided by the former class is 3-DOF active translational, whereas 3-DOF force and 3-DOF torque feedback are provided by the latter class. This family of haptic interfaces has a wide range of workspace size and force feedback capability. For instance, the workspace size and the maximum force of Virtuose 6D are $1330\times1020\times575\,\mathrm{mm}$ and $34\,\mathrm{N}$, respectively. Freedom-7 (produced by MPB Technologies Inc., Canada) is another serially-chained haptic device tailored for medical simulations [96] whose workspace is sized and is capable of providing high position resolution. This haptic device possesses a high resolution of positioning, low friction in the joints, and low apparent inertia. However, its small force feedback of up to $0.6\,\mathrm{N}$ compared to that of other haptic interfaces is notable.

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MAHI arm exoskeleton (developed at Rice University, USA) is a 5-DOF grounded exoskeleton-type haptic interface whose design objective was principally rehabilitation tasks and virtual environments-aided training [64, 97]. The majority of the workspace of the human arm can be covered by this device. Also, elbow, forearm, and wrist joints can be involved in the intended task by applying independent forces thereto. This interface is not working based on point contact, and various joints of the human can be provided with feedback that is controlled independently. Thanks to this independence, a therapist can effectively employ the exoskeleton for rehabilitation and focus the therapy on individual joints. In the same area of application, Quanser Inc. in partnership with the University of Toronto and Toronto Rehabilitation Institute (Toronto Rehab) has developed a haptic device called Autonomous Upper-Limb Stroke Rehabilitation Device for limb rehabilitation in stroke victims [98] (see figure 5).

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Ueberle et al [75] designed VISHARD6, a 6-DOF haptic interface with a workspace size of $880\times400\times310\,\mathrm{mm}$. VISHARD6 has a relatively large workspace. However, an area in the center of the workspace is not available for haptic interaction due to interior singularities. Van der Linde et al [99, 100] also described the design and control of an admittance-controlled manipulator called HapticMaster (commercialized by FCS Control Systems, Netherlands). This large-workspace ($460\times400\times360\,\mathrm{mm}$) and non-backdrivable interface is capable of providing large force and torque feedback [100]. It can reach maximum force feedback of $250\,\mathrm{N}$ with three DOFs.

Impedance-controlled and admittance-controlled devices are dual in both cause-and-effect and performance. The impedance-controlled devices usually have low weight, zero backlashes, and no stick slip while renders low mass [101]. As a result, they have poor performance around higher forces and also high stiffness and mass. Due to the weight limits of the mechanism, employing complex end-effectors is also debatable. Admittance-controlled devices, on the other hand, are able to render a high stiffness. They are decent devices for large workspaces, master-follower tasks, and carrying end-effectors that are complex and high-DOF. Given a contact, the admittance-controlled devices intrinsically record the contact forces that encounter. The limitation of these devices is often the inability to render very low mass and friction, which means that the user will always feel the inertia and friction. These haptic interfaces suffer from the small force feedback over which mechanical properties (such as apparent inertia) and the friction of the joints of the interface can cast a shadow [24]. This drawback deteriorates the resolution and sensitivity of haptic feedback for the user. Rehabilitation applications typically demand a haptic interface capable of providing high force feedback, while the resolution of the force feedback is not important as much. Therefore, the admittance-controlled haptic interfaces are mainly designed for such purposes and optimized for human interaction and most useful in cases such as virtual assembly, haptics, and robotic rehabilitation. The haptic resolution, force depth, and impedance ratio are provided as performance indicators. This device cannot render torques and need an additional 3-DOF end-effector to this end. Admittance control is also commonly used in industrial manipulators because of high forces and stiffness. Since haptic manipulators always get in touch with a human physically, safety measures such as magnetic lock, emergency stops, and the workspace should be considered seriously.

5.3. Haptic interfaces with parallel mechanism

A closed-loop linkage with at least two chains that has an end-effector and a fixed based form a parallel mechanism. The actuators are usually fixed to the base or allowed for slightly moving in the space. Several kinematic chains included in the parallel mechanism handle the load that is applied to the end-effector and distributed thereon. As a result, parallel mechanisms are typically lightweight and structurally stiff. Also, the cut-off frequency of the dynamic transmission behavior and subsequently the transmission transparency of the haptic device are high. These properties significantly attract the attention of the researchers, but some drawbacks of parallel mechanisms should be noted in the meantime. For example, the small workspace of parallel mechanisms compared to the serial counterparts is thought of as a major drawback. Due to having several kinematic chains from the base to the end-effector, the kinematics and dynamics models of parallel mechanisms are more complex and nonlinear. The closed-form solution for the forward kinematics is not available for all configurations of a parallel mechanism [43]. Further, the position of the mechanism affects the transmission behavior, resulting in a parallel mechanism being considered directional and anisotropic within its workspace. Also, designing a high-DOF parallel mechanism is complicated because it requires several universal and spherical joints, which add to the friction and backlash of the mechanism.

A haptic interface designer should carefully consider singular positions of a parallel mechanism when planning for a closed-chain haptic device. In singular positions, at least two links of the mechanism become aligned. Singularity can occur in two situations. In the first case, which typically happens at the borders of the workspace of the mechanism, the transmission of the actuator's motion to the end-effector fails. In the second case, the transmission of the actuator's force or torque to the end-effector fails. This case, which typically happens within the workspace of the mechanism, leads to the state that no load can be carried by the end-effector. Quickly changing the transmission or gear ratio happens in a mechanism close to the singular positions to the point that the mechanism becomes locked at the singular position. In fact, the mechanism loses some DOFs in a singular configuration, putting the mechanism at risk or making its control impossible. Therefore, a designer is expected to analyze the singularities of the intended parallel mechanism to certainly avoid them during operation.

HD² High-Definition Haptic Device (produced by Quanser Inc., Canada) is a haptic interface from the family of interfaces designed based on pantograph kinematics, which possesses 6-DOF position sensing and provides 6-DOF feedback [102]. Thanks to the dual-pantograph kinematics of the mechanism, the workspace is as large as $800\times250\times350\,\mathrm{mm}$ and the force and torque feedback can reach a maximum of $19.7\,\mathrm{N}$ and $1.72\,\mathrm{Nm}$, respectively (see figure 5).

Omega, Delta, Sigma, and Lambda are categories of haptic interfaces in a family of parallel haptic interfaces commercialized by Force Dimension (Nyon, Switzerland) [103, 104] (see figure 6). Although these interfaces possess a smaller workspace compared to the serially-chained haptic interfaces, they provide relatively higher force feedback. Within the family, Sigma.7 with the largest workspace size of $190\times290\times130\,\mathrm{mm}$ provides the highest level of force and torque feedback, which are $20\,\mathrm{N}$ and $0.4\,\mathrm{Nm}$, respectively, with a superior resolution of position in all six DOFs. Lambda.7 is the most recent haptic interface developed by Force Dimension possessing a larger base compared to sigma.7 and seven active DOFs in translation, rotation, and grasping. Falcon (produced by Novint Technologies, USA) is the economically-designed version of Omega.6 with a lower force feedback capability ($9\,\mathrm{N}$), resolution of position, and the workspace size of $100\times100\times100\,\mathrm{mm}$.

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Asada et al [105] introduced the planar five-bar mechanism whose advantages are simple dynamics and low inertia. The Delta mechanism proposed by Clavel [106, 107] is another 3-DOF parallel robot whose actuators are grounded. Three skewing parallelograms connect the base to the end-effector of the robot. Having an end-effector consistently parallel to the base is the main advantage of the Delta robot, which makes it a candid positioning mechanism for manufacturing applications. However, solving the forward kinematics of the Delta robot in closed-form is difficult. Hayward [108] also took the advantages of parallel mechanisms to propose a 4-DOF wrist structure in which three rotations, as well as a translation along the axis of roll rotation can be controlled.

It is worth clarifying that there might be other perspectives than ours when researchers analyze the kinematic chains of haptic interfaces that have been addressed here. As seen in some mechanisms in figures 3 and 4, a parallelogram is used in the linkage design. That parallelogram is added to transfer the torque of the actuator located on the second joint to the third link to keep all actuators close to the base link and not in serial joints. However, by parallel kinematic design in this paper, we mean mechanisms that use the torque of the actuators in parallel to have almost the same contributions on the end-effector force/torque, which is the combination of all forces/torques and will result in a higher force on the end-effector. In serial designs, the actuator of the first and second joints are located far away from the end-effector and have less effect or contribution on the end-effector force than the third joint actuator. It means, if one uses the same actuators with the same torque capacities in serial and parallel designs, the parallel one (as defined in this paper) will result in more force on the end-effector. This note is also backed by figure 2.

5.4. Haptic interfaces with hybrid mechanism

Combining serial and parallel mechanisms generates a hybrid kinematic device [109–111]. From the fixed base to the end-effector of a hybrid device, the parallel mechanism is connected to the base while the serial mechanism links the parallel mechanism to the end-effector of the device. This arrangement adds to the DOF of the end-effector. Tsumaki et al [83] designed a 6-DOF hybrid mechanism comprised of a 3-DOF parallel Delta robot [107] and a 2-DOF agile eye (a five-bar spatial mechanism) [112] serially mounted with a revolute joint. The advantage of the hybrid mechanism is providing decoupled translational and rotational motions while being easy to analyze and model kinematically. The drawbacks, on the other hand, are the inertia in motion and the volume of the robot rooted in the actuated joints of the wrist.

Delta.6 is a 6-DOF hybrid robot in which the combination of a 3-DOF wrist mounted on the end-effector of a 3-DOF parallel Delta robot [107] enables the mechanism to translate and rotate (see figure 7). Abeywardena and Chen [81] proposed the Monash Epicyclic Parallel Manipulator (MEPaM) in which a cable-pully system is used to mount all actuators to a 3-leg 6-DOF parallel robot. Possessing back-drivability and also low mass and inertia of the legs qualifies the mechanism to be used as an impedance-controlled haptic device. Taking the motion of the mechanism into account, the MEPaM suits virtual environments as a haptic device. The workspace size of the MEPam is $142.5\times171\times187\,\mathrm{mm}$. Dede et al [113] proposed a hybrid haptic device comprised of Hybrid-Spherical and R-Cube mechanisms. The kinematics of the device is easily analyzed thanks to the decoupled motions of the stated mechanisms.

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5.5. Strengths and weaknesses of the reviewed haptic interfaces

The development and implementation of evaluation methods to experimentally measure the performance of haptic interfaces has been a matter of debate since the 80s when force-reflecting hand controllers (the former name of haptic interfaces) found a place in teleoperation. In order to know the requirements of a device, the physical performance of the device should be evaluated. The performance can be evaluated by employing the measures and characteristics of robotic platforms. A haptic interface is primarily expected to command the follower side or virtual environment based on the orders of the operator and also obtain applicable sensory information, particularly forces, from the remote side and reflect it back to the master side. Operator-interface interaction must be basically free from any kind of interference rooted in the kinematics and dynamics of the device. According to Jex [115], the performance of a haptic device is approved given passing four tests. The interface passes the first test given simulating a piece of light balsa wood with small inertia and almost zero friction. Simulating a sudden hard stop is the second expectation from the device in the evaluation tests. The third test focuses on the ability of the device to simulate the Coulomb friction, meaning that the device should go to the zero-velocity state if the operator stops holding the handle. Lastly, the simulation of mechanical detents without lag and with a sudden transition in the fourth test is expected from a haptic device.

A number of other researchers also investigated the evaluation methods for haptic devices. For instance, McAffee and Fiorini [116] recognized the principal characteristics that affect the performance of the hand controllers and then compared the performance of the existing devices quantitatively. The technology of robotic actuators was comparatively analyzed by Hollerbach et al [117]. The performance measures of haptic interfaces were defined by Hayward and Astley [55] theoretically, while Morrel and Salisbury [118] worked on formalizing the performance measures for coupled micro-macro actuators. Furthermore, Ellis et al [56] demonstrated how to experimentally measure the performance of these devices.

The methodologies existing for the physical evaluation of haptic interfaces are categorized based on the properties of passive (unpowered), powered, and controlled robotic systems. The actuation-free investigation gives the space to characterize passive systems. While electronic and control elements play no role, the design of the mechanism and structure determines the properties of passive systems. The properties of powered systems, on the other hand, state how capable the actuation and sensing of the device are. This capability is identified by investigating the flow of input and output individually and separately without implementing any control algorithm. In the end, the performance of the whole controlled system is specified by forming a loop that includes the human, mechanical structure, actuation system, and sensors.

A haptic interface is basically expected to move similar to all robotic mechanisms. Kinematic analysis to find the pose and velocity of the mechanism, therefore, helps us to define how capable the mechanism is and where the boundaries of the motion are. The design of the robot, how to select the actuators, sensors, and the control method are all related to the kinematics of the interface, which includes both joint space and task space analyses. The Jacobian matrix J relates the velocities and force/torque of the robot in the joint and task spaces as

$$\begin{align} \dot X & = J(q)\,\dot q, \end{align} \tag{ 1a }$$

$$\begin{align} \tau & = J^T(q) F, \end{align} \tag{ 1b }$$

where $\dot{X}$, $\dot{q}$, τ, and F are the vectors of end-effector velocity, joint rates, joint torques, end-effector force/torque, respectively. The Jacobian is a function of the pose of the mechanism and serves as the fundamental element of the kinematic analysis of the robot. A set of factors contribute to the kinematic performance analysis of a robot, including DOFs, singularities of the robot, kinematic isotropy, workspace, and the indices of manipulability and dexterity.

• Workspace: The shape and volume of the workspace are defined based on the configuration of the mechanism. The workspace is normally represented graphically in the form of a basic shape or an envelope. The reachable and dexterous workspaces can be attributed to a robot. The setpoints reachable by the end-effector form the reachable workspace, whereas the points reachable by the robot in any arbitrary orientation represent the dexterous workspace. Early methods used numerical and algebraic analyses to define these workspaces of a mechanism. For example, Kumar and Waldron [119], Yang and Lee [120], and Tsai and Soni [121] used numerical techniques for this purpose. Numerical methods are superior to algebraic ones because they easily include kinematic constraints. The limitation of these methods is that universal principles or insights of design are difficult to reach. Gupta and Roth [122] and Gupta [123] introduced an algebraic method of workspace characterization based on topological analyses. In this method, the concept, as well as the existence conditions of holes and voids of the workspace are first presented. They also analyzed what shape the dexterous and reachable workspaces may have. Further, Freudenstein and Primrose [124] and Lin and Freudenstein [125] studied the workspace analysis, precisely developed relationships between the kinematic parameters and workspaces, and optimized the workspace volume of a class of manipulators that have three joints. Then, Vijaykumar et al [126] analyzed workspace optimization in a more general way. They defined the performance of the manipulator in terms of the dexterous workspace and showed that the elbow manipulator is the optimal six-revolute (6R) mechanism if a set of constraints on the Denavit–Hartenberg parameters are satisfied.
• Dexterity: Moving and applying torques and forces in arbitrary directions indicates the dexterity of a manipulator. The dexterity can be measured based on several performance metrics. The term manipulability, introduced by Yoshikawa [59], is defined as:
  $$\begin{align} \mathcal{M} = \sqrt{\textrm{det}(JJ^T),} \end{align} \tag{ 2 }$$
  which quantitatively shows to what extent the manipulator can arbitrarily change the pose for a given posture without any difficulty. A measure of distortion ascribed to the Jacobian was proposed by Salisbury and Craig [127]. The largest singular value $\sigma_{\textrm{max}}$ of the Jacobian divided by the smallest singular value $\sigma_{\textrm{min}}$ defines the condition number, κ,
  $$\begin{align} \kappa = \frac{\sigma_{\textrm{max}}}{\sigma_{\textrm{min}}}. \end{align} \tag{ 3 }$$
  Near the singularities of a manipulator, the condition number advances toward infinity. Thus, using the reciprocal of the condition number, 1/κ, which is limited to [0, 1] is more convenient. The dependency of the condition number to the pose of the robot is a source of local information about the dexterity. Integrating the condition number over the entire workspace [128, 129] introduces the global conditioning index (GCI) as:
  $$\begin{align} \eta = \frac{\int \frac{1}{\kappa}dW}{\int dW}, \end{align} \tag{ 4 }$$
  which is a more general metric compared to the condition number. The movement isotropy of the mechanism over the workspace is represented by the GCI. If the GCI approaches 1, the even feel becomes more through the workspace [130].
• Structural stiffness: High structural stiffness in a robot is an asset because the position of the end-effector is reliably calculated given stiff links and joints and also the structural response of the robot is better when loaded dynamically. In order to measure the structural stiffness of a haptic interface, which is usually performed at the endpoint, the joints should be locked. By putting a loading typically a dynamometer on the endpoint, a dial indicator placed at the same point measures the deflection of the system. Therefore the structural stiffness of the system can be calculated as applied force divided by the deflection of the system along the direction of the applied force.
• Apparent inertia: Asada [131] and Khatib [132] introduced the concept of generalized inertia ellipsoid (GIE) as the geometric shape formulated by:
  $$\begin{align} \Lambda = (JM^{-1}J^T)^{-1}, \end{align} \tag{ 5 }$$
  where M stands for the matrix of inertia in the joint space. The formulation describes the dynamic capability of a robotic mechanism. Apparent inertia, in a haptic interaction, states how much inertia the operator feels while moving the end-effector.
• Force feedback capability: The manufacturer of a device is usually expected to provide the maximum capability of the device to produce output in static conditions. The maximum force that a haptic interface can produce is of the same nature. This metric is specified by either transient peak force or maximum continuous force. Heat dissipation limits the duration of the former force. Therefore, the latter force is a better metric to evaluate the performance of haptic devices. To this end, designers are willing to identify the maximum force that a haptic interface can apply to the operator's hand. The Jacobian matrix relates the motor torques, τ, to the forces/torques applied to the endpoint of the robot, F, according to:
  $$\begin{align} F = (J^T)^{-1}\tau = J_F\tau. \end{align} \tag{ 6 }$$
  Therefore, the bounds of the force given a unit torque vector ($\left\lVert\tau\right\rVert = 1$) are defined as [23]:
  $$\begin{align} \sigma_{\textrm{min}}(J_F)\leqslant \left\lVert F\right\rVert\leqslant \sigma_{\textrm{max}}(J_F). \end{align} \tag{ 7 }$$
• Sensitivity: In a haptic interface, (6) gives the motor torque required to generate a desired force at the end-effector. The encoders of the interface usually measure the current position relative to the position of the interface after restart (zero position). The home position is also where the arms and motors are at the right angles with respect to each other [133]. If any offset between the zero and home positions appears in the forward kinematics and the Jacobian matrix, the measurement of q_i becomes erroneous, which in turn deviates the actual force reflected to the operator from the intended force. Suppose that all encoders of the interface have a small offset error, δ, in their measurements as:
  $$\begin{align} \hat{q}_i = q_i+\delta, \end{align} \tag{ 8 }$$
  where $\hat{q}_i$ and q_i are the measured and actual positions, respectively. Relying on (6), the torque of the motors relates to the intended and actual force feedback as:
  $$\begin{align} \hat{F} = J_F(\hat{q}_i)\tau \ \text{and} \ F = J_F(q_i)\tau. \end{align} \tag{ 9 }$$
  The normalized error of the force feedback is calculated as: [23, 134]
  $$\begin{align} \gamma = \frac{\left\lVert \hat{F}-F\right\rVert}{\left\lVert F\right\rVert}. \end{align} \tag{ 10 }$$
  Considering the small offset error, a Taylor series expansion around q_i gives $J_F(q_i+\delta)\approx J_F+\delta J^1(q_i)$ resulting in:
  $$\begin{align} \gamma = |\delta | \cdot \left\lVert J^1\tau\right\rVert/\left\lVert J_F\tau\right\rVert. \end{align} \tag{ 11 }$$
  Given $\left\lVert \tau\right\rVert = 1$, without loss of generality, a normalized force feedback error of $\gamma \leqslant \gamma_1$ requires the initial error, δ₀, to satisfy $\delta_0\leqslant \min \frac{\sigma_{\textrm{max}}(J_F)}{\sigma_{\textrm{min}}(J_F)}$. In addition, the normalized force feedback error in the case of initial angle offset of δ₀ is limited at each point within the workspace of the device according to $\gamma \leqslant |\delta_0| \frac{\sigma_{\textrm{max}}(J_F)}{\sigma_{\textrm{min}}(J_F)}$.

Kinematically redundant haptic interfaces are possible solutions to deal with the design trade-offs stated in the previous sections. The number of DOFs in such manipulators is higher than what is needed to perform a task successfully. In a haptic interface possessing joint space redundancy, inner joint motion, which is also called self-motion, is feasible. It means that one can move joints while the pose of the end-effector remains unchanged. An interface can be expected to fulfill primary and secondary tasks at the same time [135]. Position, force, or impedance control of the manipulator in the task space are the examples of primary tasks while the robot is expected to avoid singular points in the workspace, reach a higher manipulability, or maximize the force feedback as the secondary objectives. This redundancy is present in the human arms and fingers as well [136]. As reported by Schaal and Schweighofer [137], complex dexterous tasks given to human users are performed by utilizing kinematic redundancies in the arm accompanied by a compliant control in the task space. Nisky et al [138] also studied the performance of experienced surgeons and reported that arm redundancy is employed by skilled surgeons more than the novice counterparts to stabilize hand movements.

Redundant manipulators have been widely used in industrial sectors [139]. Ficuciello et al [140] reported the benefits of the self-motion in the control of physical human-robot interactions because it improves interaction performance as a secondary objective. Despite having desirable features, the design and control of redundant haptic interfaces (RHIs) have not captured the attention of the community at a high level. The community has been majorly focused on the application of redundant robotic arms in object manipulation tasks or physical human-robot interactions in industrial domains. A range of reasons may be counted for the few studies conducted on the RHIs design. Compared to a non-redundant haptic interface (NRHI), a higher number of joints, links, and actuators add to the design complexity and cost as well as the required computational power of an RHI. The higher computational power is the consequence of the demand for a complex algorithm to control the extra DOFs. The mechanical design of industrial robots is mainly focused on enabling the robot end-effector to move quickly or carry large payloads. The design of a haptic interface, on the other hand, should satisfy these two opposing requirements while possessing back-drivability and also low apparent inertia and friction. That is why the design of haptic interfaces is more constrained, and their design and control are more challenging.

To the best of our knowledge, the only commercially available haptic interface is the user interface of the da Vinci Surgical System (Intuitive Surgical Inc.), but no design-related information is available for proprietary reasons. The user interface of the da Vinci Surgical System is described in [141]; however, there is no quantitative information made available. The redundant user interface of the system has an extra DOF that is meant to allow the handle of any tool attached to a follower device to move in space in ways similar to the motions that a surgeon might use with their tools in a non-robotic surgery. A processor shoulders the responsibility of actively driving the extra DOF of the device to keep the device far from the singularities [141]. In the da Vinci master interfaces, it is debatable whether these qualify as haptic interfaces. Although the redundant linkages of the master hand controllers are actuated, the actuation does not correspond to the sensed properties of the follower manipulators. However, they are included in this paper as they have the potential to provide haptic feedback to the user and thus can be considered as haptic interfaces. Further, as far as we know, the only paper on the design of a redundant haptic interface is [82]. VISHARD10 has a relatively large workspace of cylinder $1700\times1700\times600\,\mathrm{mm}$ with the maximum force feedback of $170\,\mathrm{N}$. In comparison to the data available in table 2, VISHARD10 has both a larger workspace and a larger force feedback capability.

As the RHIs are still in their infancy, there are not much data available for quantitative comparison of redundant and non-redundant haptic interfaces. Regardless, the RHIs have intrinsic advantages over NRHIs in terms of better kinematic and dynamic characteristics, for example, increased manipulability (one result of which is reduced friction) and reduced apparent impedance [24]. The intrinsic advantages of RHIs over NRHIs in terms of meeting the criteria in section 4 has been investigated in [24]. These advantages depend on the kinematics and dynamics of RHIs, not on any algorithm or computer-based control. Manipulability index, the size of the workspace, and the accuracy of force feedback, which are measures of the kinematic performance, in RHIs can reach a level higher than those of the original NRHIs by only adding to the DOFs of the base. Additionally, the measures of the dynamic performance, which are apparent inertia and friction, in the RHIs are at a lower level compared to the NRHIs [24]. The closed-loop control of the RHIs at the joint level is benefited from the redundancy to satisfy secondary objectives. A null-space controller, in parallel to the main controller devised for primary objectives, attempts to achieve secondary objectives. By manipulating the extra DOFs of the interface properly, the RHI redundancy is able to decrease the reflected friction of the joints at the end-effector [142]. As a result, the haptic feedback resolution, also called sensitivity, will be increased for the user. A psychophysical experiment conducted in a simulated soft tissue palpation task validates how much the force perception of the user has been improved [24]. The effect of redundant and non-redundant user interfaces on the perception of the virtual stiffness is evaluated by conducting perceptual experiments. Experimental results reveal that the ability of the user to discriminate the stiffness of the tissue is enhanced by employing the redundancy in the haptic interface and mitigating the distortions rooted in the kinematic and dynamic properties of the interface.

Without adding to the length of the links of the RHI, Baser et al [143, 144] designed a 7-DOF RHI whose workspace was fairly larger than that of 6-DOF NRHIs. Adding one extra DOF to the base of haptic interfaces to in turn add to the size of the workspace was proposed by Barrow and Harwin [145], Kim [146], and Gosselin et al [147], but the redundancy resolution was not debated in their report. The teleoperation of a redundant robotic manipulator was studied by Nath et al [148] by employing an RHI with the same number of DOFs.

Actuation redundancy, which is exclusively for parallel robots [149], is another debatable category of redundancy in the haptic interface design [150–153]. Compared to parallel robots, serial robots have a larger workspace and straightforward closed-form forward kinematics solutions. On the contrary, parallel robots can produce higher force feedback, and rendering an environment with high stiffness is possible by incorporating the actuation redundancy. However, the actuation redundancy enforces a limit such that the apparent inertia and reflected friction at the robot end-effector increases due to having actuators in place of passive joints. Further, the forward kinematics of parallel robots should be solved numerically, which is computationally inefficient.

The redundancy resolution problem in redundant robots deals with how to determine the motions of the joints in order to achieve sub-tasks in the joint space in parallel to the primary task in the Cartesian space [154]. This problem is solved for the standard redundant robots in a broad range of methods among which reduced gradient-based method [155], damped least-squares inverse Jacobian method [156], and the weighted inverse Jacobian method [157] that can be extended to the RHIs. The sub-tasks include but are not limited to avoiding joint limit [158], obstacle, and singularity [59, 159] as well as maximizing manipulability. Joint velocity, acceleration, or the torque of RHIs in the null space of the Jacobian matrix can be adjusted without affecting position, velocity, the force/torque of the end-effector, which in turn results in the self-motion [160]. Hence, as the second task in some applications, a suitable auxiliary function is designed to control the self-motion and a sub-task.

Torabi et al [142] developed a null space controller for the RHIs that uses a previously-introduced index of teleoperation manipulability in [25]. The controller matches the kinematics of the RHIs to that of the follower robot to reach a higher teleoperation performance. The controller also modulates the redundant DOFs of the interface to reshape the ellipsoid of manipulability toward that ellipsoid of the follower robot. This ellipsoid, in fact, shows the kinematics of the robot geometrically. The kinematics of the haptic interface and the follower robot is matched by reshaping the manipulability of the haptic interface. The redundancy of the RHI allows us to increase the manipulability of the RHI-follower system and transfer the dexterity of the follower robot to the user more intuitively. The performance of the suggested control method is experimentally validated, which demonstrates that the null space controller empowers the user to control the force or velocity of a surgical robot and keep the control effort needed to perform a teleoperated task at a minimum.

A contact-aware null-space controller for RHI is proposed in [161]. They first introduced a task-dependent null-space controller that controls the internal motion of the RHI decently to reach the desired performance. The desired performance is reaching a low level of back-drive friction given free-space motion and soft contact, or a high level of force feedback given stiff contact. By developing a transition method, they adapted the varying objectives of the null space controller according to the task. The discontinuities of the control signal are stopped using the transition method. To keep an eye on the distance of the joint torques from the saturation levels and inform the transition method, an actuator saturation observer is proposed. Caused by the proposed controller, the feelings of soft and hard contacts can be recreated with a fidelity that is higher than that of a conventional NRHI. The effectiveness of the controller is verified experimentally in three phases of soft contact, hard contact, and transition.

By leveraging the kinematic redundancy of the interface, Torabi et al [162] proposed an actuation saturation compensation method to enable an RHI to produce better force feedback. The method is focused on the null space of the Jacobian of the RHI, taking the extra torques of actuators, and distributing them among the available yet unsaturated actuators at the joints. The method equips the haptic interface designers with the ability to use smaller actuators with lower motor inertia and friction. These properties are beneficial since the interface should be essentially low apparent inertia and friction to be able to candidly recreate the feeling of free space motion. Thanks to the proposed method, the torque that is required to render a stiff environment can be distributed among small-capacity actuators optimally. The actuators are subject to saturation without the distribution. In addition to the force reflection and actuator saturation compensation that are respectively the primary and secondary objectives, the enhancement of the manipulability of the RHI toward the direction of the task is also proposed as the tertiary objective. The latest objective acts given the first and the second objectives are possible to succeed, and the interface still has redundancy available. A four-DOF planar haptic interface is used to experimentally verify that the control of the interface using the method is practical.

A variety of interesting and novel technologies have been developed in recent decades to actuate non-linkage-based haptic interfaces. These actuators can work based on vibration, acoustics, electrostatic friction, magnetic interaction, magneto-rheological fluids, soft materials, or shape memory alloys. Though these actuators are mostly not yet commercially available, their potential in developing portable haptic devices is very high. Although our review on the design of linkage-based haptic interfaces cannot thoroughly span the range of these interfaces, we see up-and-coming trends in the community toward the design of these haptic devices as well. These technologies are briefly introduced in this section as follows.

8.1. Vibration-based haptic interfaces

8.2. Acoustics-based haptic interfaces

8.3. Electrostatic friction-based haptic interfaces

8.4. Magnetic interaction-based haptic interfaces

8.5. Magneto-rheological fluid-based haptic interfaces

8.6. Soft material-based haptic interfaces

8.7. Smart material-based haptic interfaces

8.8. fMRI-based haptic interfaces

8.9. Magnetic levitation haptic interfaces

8.10. Wearable haptic interfaces

There are unavoidable trade-offs involved in optimizing design specifications when conforming to a specific application. In teleoperated surgery, for instance, the maneuverability, sensory feedback, DOF and workspace of the haptic interface should, if possible, match the intuitive understanding of the surgeon as regards what would be their hand's in-person workspace to best emulate for them conventional surgery. Designing a new interface or selections from commercially available choices is, therefore, an application-driven process; a detailed analysis of the specific surgical application is required to determine the specifications of the interface [2]. The following general specifications concerning telesurgery have been determined by analyzing freehand surgery in a conventional environment.

• An interface's end-effector needs a minimum number of DOFs for the task it must be used to perform in Cartesian space. Most surgical applications require 7 DOFs; 3 for orientation, 3 for translation, and a final one for grasping motion. Some surgical applications, however, require lower DOFs for the end-effector. An example of this would be needle insertion, which is a 5-DOF action (3 DOFs for translation and 2 for orientation) [2].
• The interface's haptic feedback mechanism should ideally contain the same number of DOFs for force and torque feedback as the number of DOFs of the end-effector, but in actuality, this number is a trade-off between cost, interface complexity, and the level of benefit involved in receiving the feedback. Additionally, the end-effector of the follower's existing force and torque measurements determine the maximum force and torque feedback DOFs for the haptic interface. As well, some haptic feedback DOFs can adequately and cost-effectively be replaced by graphical cues. While many studies show that haptic feedback is beneficial [89], some have found in at least some instances that task performance and accuracy can be comparable when relying instead on graphical cues [2, 44].
• For sensing position and orientation of the end-effector, the resolution needed must suit the surgical application. For example, ablation of a brain tumor necessitates sub-radian and sub-millimeter precision, a resolution that must be sensed by the interface and passed on correctly to the follower [2].
• The interface requires a workspace large enough to make certain that an action can be taken, along with one free of singularities. Therefore, motion scaling between the follower and the interface is quite important and requires close attention. As well, the footprint-to-workspace ratio of the interface needs to remain small enough for ease of integration and mobility within the operating theatre [2].

Those interfaces that satisfy more stringent requirements would provide better performance, but such devices are expensive, more complex than necessary, and computationally expensive for real-time control. A more cost-effective and straightforward method than designing a new interface to fabricate is using a commercially available interface purchased and modified as needed. This, however, means that not all the characteristics of the interface will be accomplished. Haptic interaction fidelity perhaps becomes limited due to the few minor alterations that might be made to commercially available interfaces. If an appropriate commercial device does not yet exist, in the instances of more sensitive uses such as telesurgery, it may be best to design a new device specific for the application rather than risking patient safety. However, some less risk-critical medical tasks, such as rehabilitation, could be performed with the use of modified commercial devices [2].

There are some metrics in the literature for performance evaluation of haptic devices that can be categorized into two sets [209]. One is the performance evaluation based on user studies, which is highly dependent on the application in which the haptic device is used. In these studies, some tasks are designed similar to the actual task in that intended application to be performed by human subjects, collect the data, analyze the data based on some measures such as task completion time, number of errors, the maximum force applied, quality of the task performed (by measuring the blood loss in surgical tasks, for example), and other relevant factors [210]. The results of that analysis can be used as a measure for the haptic device performance. Although this analysis and the corresponding results depend on the mechanism or kinematic design of the device, there is no direct or clear correlation between these two factors.

The second set of measures are more related to the physical characteristics and specification of the haptic device, such as workspace, manipulability, force generating capability, minimum controllable force (force resolution), maximum force, stability, low apparent inertia, low friction, back-drivability, redundancy, global positioning index, and many more factors [211]. To the best of the authors' knowledge, there is no systematic method proposed in the literature to optimize the mechanism design to meet a specific set of constraints. Most of these quantitative measures are highly application-dependent. For example, while higher force feedback capability might be very important in one application (e.g. in manufacturing dealing with high forces), it might not be as important in another application (e.g. in brain surgery dealing with low forces) [212, 213].

The design and development of haptic devices enabled many users to have a two-way interaction with machines. While they can be used to provide input commands (e.g. position or velocity commands for a surgical robotic system), they provide haptic or tactile feedback to the users' hands by pushing back on them and providing a sense of telepresence for the users. While visual or auditory sensory feedback can be considered the most important, haptic feedback provides an additional link to the users that can improve the quality of task performance. Despite many potential advantages of these devices, there have been many challenges in designing, developing, controlling, and adopting these devices in many applications.

The adoption of haptics technology has been very slow and many companies have been hesitating in incorporating this technology in their products. There is still an ongoing debate on the advantages and safety of such technologies in medical robotic systems. The interaction with hard objects such as bone tissue might introduce instability in the system. This problem becomes worse when there is a delay in the communication link between the local master haptic device and the remote follower robotic arm. There have been many efforts in addressing this issue by providing many control strategies such as the passivity approach, yet, it is still an open problem, and many researchers are providing new solutions.

Another challenge in adopting haptics technology in medical robotic systems is the acceptance of such technologies by healthcare providers, including surgeons. They might argue that the force feedback provided by these devices might distract them and limit their autonomy in performing delicate tasks in surgery. One possible solution to mitigate that problem is to provide high-quality surgical simulators and virtual reality systems for surgeons to compare their performance with and without haptic feedback. These simulators can potentially change their preference towards adopting haptics technology in their tools, such as robotic surgical systems.

The cost and complexity of haptic devices are also other challenges in this regard. The high cost of developing haptic devices causes the manufacturers and companies' hesitation in incorporating such devices in their products. There have been recent efforts in the development of high-quality and low-cost haptic devices. These efforts provide a promising future for haptic technologies by increasing the demand and decreasing manufacturing costs. In medical robotic systems, many major companies such as Intuitive Surgical, which commercializes the da Vinci Surgical System as the most popular robotic system in the world, are working on providing high-quality haptic feedback in their workstations for surgeons. As many patents of the da Vinci Surgical System are more than 20 years old and are expiring, other companies have made tremendous efforts in the design and development of new robotic surgical systems for medical communities to be used in different surgical and medical applications. One selling point of such novel systems can potentially be their workstation. The workstation of a medical robotic system is arguably the most integral part of the system as it connects the surgeon to the surgical site and tools. If misdesigned, it can degrade the quality of healthcare and cause complications. Ease of use, intuitiveness, and ergonomics are the main contributing factors. This workstation can be compared to its counterpart, the cockpit of an aircraft. The information provided to the surgeon by the workstation is used and processed by the surgeon to plan and execute the next move. Haptic feedback is arguably the most important sensory feedback after visual feedback. Surgeons rely on their judgment and their brains' high decision-making capability to make the next smart move. Every move in surgery can be the difference between life and death. Haptics technology can help surgeons to make a much more informed decision. This fact has been realized by many companies developing surgical robotic systems as a promising future direction.

Despite all efforts by design engineers, researchers, manufacturers, companies, knowledge users (e.g. surgeons), and others in the field of haptics concerning the design and development of novel haptic devices, there remains much work to do. This review paper shows the importance of this field for researchers and the possible gaps in the literature and knowledge. The kinematic design of various linkage-based haptic devices by researchers, which were explained in this paper, shows that there is no ideal haptic device that can be utilized for all or most applications. Each application, depending on the operator or end-user requirements, dictates the initial design of a new haptic device based on the experience of other designers. In medical applications, the most important factor is the acceptance and approval of the end-users (surgeons and healthcare providers), which in turn guarantees the success of the design. There are trade-offs between the desirable characteristics of haptic interfaces, such as maximum force feedback capability vs. minimum inertia or maximum stiffness vs. workspace size. Indeed, a large force feedback capability requires large actuators, which increases the HI's inertia. A large workspace requires long links, decreasing the HI's stiffness and increasing its inertia. Therefore, the design of haptic interfaces has to be optimized for a specific application. These design trade-offs can be relaxed by adding redundancy in the haptic interface mechanical design. Also, the kinematic and dynamic characteristics of redundant HIs can be further optimized through closed-loop control to reconfigure and adapt RHIs based on information about the task. This paper is an effort in providing a comprehensive review of linkage-based haptic devices for researchers and engineers and might help them in their design and development endeavors.

This work was supported by Canada Foundation for Innovation (CFI), the Natural Sciences and Engineering Research Council (NSERC) of Canada, the Canadian Institutes of Health Research (CIHR), the Alberta Advanced Education Ministry, the Alberta Economic Development, and Trade and Tourism Ministry's grant to Centre for Autonomous Systems in Strengthening Future Communities.

No new data were created or analyzed in this study.