Design and Analyses of a Novel Reconfigurable Logging Branch Mechanism

A reconfigurable logging and branch-lopping mechanism has been designed to shorten the production cycle, reduce work intensity, and improve labor survival rate in the logging industry. The mechanism integrating logging and branch-lopping functions can flexibly morph into three con-figurations, namely, series, parallel and mixed, as well as eight structure states to satiate different requirements. Not only does it possess sufficient stiffness to fell large trees but it also offers high flexibility to trim and crop small branches which superior performance has relatively wide engineering application prospects. The kinematics and static stiffness of the mechanism are the key techniques for its engineering application. With the mechanism as the research object, the working principles were analysed and the adjacency matrix of each structure state was presented. The Screw Theory and CGK formula were deployed to calculate the degrees of freedom of some of the structure mechanisms. The kinematics of some of the structure states was analysed and their flexibility matrices were obtained with vector algebra. The static stiffness of two structure states was compared indirectly by contrasting their flexibility matrices before their kinematics was simulated numerically. Engineering application of the mechanism in welding robots, robots that pick up objects, cleaning robots and other fields is demonstrated towards the end of this paper.


Introduction
As one of fundamental industries, forestry can become the symbol of the country's strength and prosperity via mechanization and automation.Decades ago, timber production machinery could only offer one operation method [1][2][3].Since the US, Finland and other countries started to conduct researches on multitasking timber harvesters operating in timber production areas and after arduous studies created a multitasking timber harvester that offered 2 operating methods for each task, including logging and timer-piling machines as well as logging and branching-lopping machines [4,5].Later northern Europe invented a small size logging and timber-piling machine which can fell trees for timber and crop branches.The Finnish company Plustsh integrated walk technique into timber production machinery by creating a six-legged timber production machine.The development of multitasking timber harvesters operating in timber production areas not only boosted production efficiency and guaranteed the safety of the workers but also brought an indispensable impetus to the economic development [6][7][8][9][10][11].
Although multitasking timber harvesters operating in timber production areas have been upgraded in recent years, the innovative designing method for and theoretical research on timber production machinery still remains weak [12][13][14][15][16][17].In this paper, the methods from modern mechanisms that create reconfigurable mechanisms are applied to the design of the logging and brand-lopping mechanism which present a novel logging and branch-lopping mechanism.The novel mechanism, which integrates the logging and branch-lopping functions, can flexibly morph into three configurations, namely, series, parallel, and mixed, as well as 8 structure states to satiate different requirements.Not only does it possess sufficient stiffness to fell large trees but it also offers high flexibility to trim and crop small branches.The novel mechanism's superior performance has relatively wide engineering application prospects.The kinematics and static stiffness of the mechanism are the key techniques for its engineering application.With the mechanism as the research object, its working principles were analyzed and the adjacency matrix of each structure state was presented.The Screw Theory and CGK formula were deployed to calculate the degrees of freedom of some of the structure mechanisms.The kinematics of some of the structure states was analyzed and their flexibility matrices were obtained with vector algebra.The static stiffness of two structure states was compared indirectly by contrasting their flexibility matrices before their kinematics was simulated numerically.Engineering application of the mechanism in welding robots, robots that pick up objects, cleaning robots, and other fields is elaborated towards the end of this paper.

Design and Analysis of Configuration
The kinematic pairs and links of the logging branch machine proposed in this paper can be flexibly reconfigurable into 8 structure states.A moving rotating motion pair, whose transformation is the key to the state transformation of the logging branch mechanism, forms the basis of this design.Both the first side rod and the first sliding rod, as well as the second side rod and the second sliding rod, are connected by means of moving rotating motion pair.Figure 1 depicts the initial structural state of the mechanism and a schematic diagram of the connection between the first side rod and the first sliding rod, as well as the operation of the moving rotating motion pair.

The revolving block
The first sliding rod One of the most crucial elements of this design is the moving rotating motion pair which is one of the critical reasons why the mechanism can flexibly morph into different structure states.One moving rotating motion pair connects the first side rod and first sliding rod, while the second moving rotating motion pair connects the second side rod and the second sliding rod.The moving rotating motion pair structure in figure depicts how the first side rod and first sliding rod are connected, especially how the pair functions.
The upper half of the revolute pair ring is welded to one end of the first side rod.The lower half of the revolute pair ring is installed onto the upper half via the former's circular slots.The lower half can spin around the upper half.The middle section of the first side rod has a sliding track into which the first sliding rod is installed.The first sliding rod can slide along the sliding track inside the first side rod, thus creating the moving pair.A revolving block is welded to one end the sliding rod.When the first sliding rod slides and reaches the end of the first side rod that has the upper half of the revolute pair ring, the upper half of the revolute pair ring stops the first sliding rod from going out of the first side rod.At that moment, the lower half of the revolute pair ring is spun to surround the revolving block and the moving pair is changed into a revolute pair.The switching of kinematic pairs and the rearrangements of links allow the logging branch machine to have 8 different structural states, which are shown in figure 2.  Among the eight structure states, the ones in initial structural state, second structural state, third structural state, and fifth structural state are parallel configurations, and the fourth structural state, seventh structural state, and eighth structural state are mixed configurations with the sixth structural state being a series configuration.The logging branch machine can transform between series, parallel, and mixed configurations.The spin method is used to calculate the degrees of freedom for the structural state, with the sixth structural state having 2 degrees of freedom and the remaining 3 degrees of freedom.

Flexibility Matrix Analysis of Structural State Stiffness of Logging Branch Mechanisms
The purpose of calculating some of the structure states' flexibility matrices is to indirectly compare the stiffness of each structure state.The higher the flexibility is, the more dramatically the shape of the mechanism changes.On the contrary, the lower the flexibility is, the less the change in the mechanism's shape is.Therefore, flexibility and stiffness are inversely correlated.When the mechanism's flexibility matrix is being obtained, the inverse matrix is unnecessary and the difficulty of the calculation is reduced.Therefore, the flexibility matrix is employed to indirectly compare the stiffness between some structure states of the mechanism.The original, fourth, fifth, and sixth structure states are selected as the research subjects.It is assumed that the kinematic pair represented by ( ) The formula for calculating the flexibility matrix is shown in equation ( 1).
In equation ( 1), J is the Jacobian matrix of velocity and  is the matrix of the Hookean Spring constants of the kinematic pairs of the mechanism.
The Jacobian matrix of velocity for the original structure state is 1 J .In the original state, the matrix of the Hookean Spring constants of the kinematic pairs of the mechanism in the original structure state is described in equation ( 2).
The flexibility matrix of the original structure state, 1 C , is shown in equation (3).
In equation ( 33), ( ) The Jacobian matrix of velocity for the fourth structure state is 2 J and the matrix of the Hookean Spring constants of the kinematic pairs of the mechanism in the fourth structure state is described in equation ( 7).
The flexibility matrix of the fourth structure state, 2 C , is described in equation (8 The Jacobian matrix of velocity for the sixth structure state is 3 J and the matrix of the Hookean Spring constants of the kinematic pairs of the mechanism in the sixth structure state is described in equation ( 12).The flexibility matrix of the sixth structure state is shown in equation (13).
In equation ( 13),  C are obtained, the flexibility matrix of the fifth structure state is described in equation (17).
Under the assumption that    ==, when ( )

12
CC  .At this particular moment, the static stiffness of the mechanism in the original structure state is lower than that in the fourth structure state.Conversely, when ( )

12
CC  .At this particular moment, the static stiffness of the mechanism in the original structure state is higher than that in the fourth structure state.However, the stiffness of the original state and the fourth structure state are lower than that of the fifth and sixth structure state.The sixth structure state, which is a parallel structure with relatively high stiffness, is a great option for logging tree trunks with a smaller diameter.The fifth structure state which has higher stiffness is perfect for logging tree trucks with a larger diameter.The fourth structure state can lop smaller branches and the original structure can lop larger branches. .In Matlab simulation, the position curves on the x axis for the original, fourth, and sixth structure states are shown in figure 3 and the position curves on the y axis for the original, fourth, and sixth structure states are shown in figure 4. The velocity curves on the x axis for those three structure states are shown in figure 5 and the velocity curves on the y axis for those three structure states are shown in figure 6.From figure 3 to figure 6, it can be detected that the original and fourth structure states have higher velocities and therefore they are ideal options for lopping branches.The velocity of the sixth structure stare is stable and hence it is ideal for logging tree trunks.

Workspace Simulation of Structural States
The workspace of the mechanism is also one of the essential elements of the mechanism's kinematics.Therefore, the workspaces of three structure states are analyzed.The largest range for 11     From figure 7 to figure 9, it can be seen that the original state has the largest workspace and is ideal for lopping branches.The sixth structure state has relatively small workspace and is ideal for logging tree trucks.The fourth structure state has a workspace smaller than the original structure state's workspace and larger than the six structure state's workspace and therefore the fourth structure state can be deployed for both logging tree trunks and lopping branches.

Conclusions
To improve the efficiency of timber production, a logging and tree lopping mechanism that can morph into eight structure states was designed in this paper.The mechanism flexibly changes its structure states as per different working requirements and possesses high adaptability and flexibility.The reconfigurable mechanism can be applied in the timber production industry and can boost the development of multitasking timber harvesters operating in timber production areas.
The adjacency matrices can describe the connections between the structure states.Comparative analyses were conducted to understand the kinematics and static stiffness of some of the structure states so that the mechanism can be employed in engineering applications.
The mechanism is highly reconfigurable.Not only can it be applied in the timber production industry, it can also be employed in various fields, namely welding robots, robots that pick up things, cleaning robots, palletizing robots and so on.

Figure 1 .
Figure 1.The schematic diagram of the mechanism's original structure state and the moving rotating motion pair structure.

Figure 2 .
Figure 2. The schematic diagram of the eight structure states.

1 $ 1 , 4 1 $i
,5, 6 i i = has a Hookean Spring constant represented by 1 k .also represents the amount of degrees at which the kinematic pair represented by 1 $ i spins.The kinematic pair represented by ( ) also has a Hookean Spring constant represented by 3 k .The Hookean Spring constant of the prismatic pair is h k and ' h k is the Hookean Spring constant of the revolute pair into which the prismatic pair is changed.
During position and velocity simulations, under the conditions that 1

Figure 3 .
Figure 3.The position curves on the X axis.Figure 4. The position curves on the Y axis.

Figure 4 .
Figure 3.The position curves on the X axis.Figure 4. The position curves on the Y axis.

Figure 5 .
Figure 5.The velocity curves on the X axis.Figure 6.The velocity curves on the Y axis.

Figure 6 .
Figure 5.The velocity curves on the X axis.Figure 6.The velocity curves on the Y axis.

 0 ,
2 .Hence, the workspaces of the original, fourth and sixth structure states are respectively shown in figure7, figure8, and figure9.

Figure 7 .
Figure 7.The workspace of the initial structural state.

Figure 8 .
Figure 8.The workspace of the fourth structural state.

Figure 9 .
Figure 9.The workspace of the sixth structural state.

structural state Second structural state Third structural state Fourth structural state Fifth structural state Sixth structural state Seventh structural state Eighth structural state
).