Kinematic analysis of the windshield wiper mechanism with two parallel rocker blades

The paper deals with a windshield wiper mechanism with two parallel rocker blades having a complex topological structure. In the first part of the paper, the mobility of the mechanism is analyzed by means of the simplest formula for planar linkages. Also, the topological structure consisting of adyad and a tetrad has been outlined. In the second part of the paper, a kinema-tic analysis of the multi-contour mechanism is performed, the angular displacements of the two rocker blades being obtained. In this regard the independent contour method has been used, the angular displacements of all kinematicelements of the mechanism being calculated. Moreover, the displacement systems have been derived in order to obtain the velocities and late-on the accelerations of the mechanism elements. Finally, the paper ends with the displaying of the kinematic charts of the mechanism elements of which those with themovement of the two parallel rocker blades are the most wanted. This is due to the requirement of maximization of the wiping surface which is a very important safety issue.


Introduction
The importance of the windshield wiper mechanisms has been emphasized by many authors in their researches [1].For instance, S. Ciunel in his book "The driving system and modern devices for insuring the vehicle safety" (in Romanian) outlines that, among other mechanisms and devices, the windshield wiper mechanisms are directly linked to the way in which the driver receives information on traffic situation.
At the same time, the windshield wiper mechanism has an important role in the accident prevention by placing it according to the driving post design (accomplishing the anatomic, physiologic and psychologic proper conditions), according to the report "The evaluation on traffic safety in Romania" (in Romanian) by C. Uta, Romanian Automotive Register.
There are several types of windshield wiper mechanisms of which two types, i.e. those with "parallel" blades and with opposite blades, are the most used on passenger motor vehicles [9].
From the very beginning a simplifying hypothesis has been imposed: the windshield wiper mechanism with two parallel rocker blades studied in the paper to be a planar linkage.This is due to no more than 5° angle between the two fixed rotate axes of the "parallel" rocker blades that exists in reality in usual passenger motor vehicles.That means that apart from the three rotate joints (the two pairs between the rocker blades and the car body, and the articulation between the crank and the car body) the real -mechanism has spherical joints.Therefore, the analyzed mechanism has only revolute joints (figure 1).This special type of wiper mechanism has a complex structure having seven articulated elements of which the crank 1 is the driving element, and the rockers 3 and 7 are the driven elements on which the wiper blades 3' and 7' are attached.The mechanism is mounted in the vehicle body denoted with 0 as fixed element.
The mobility of the planar mechanism is calculated by means of the formula [4, 5]: (bi-mobile kinematic joints).By substituting these numerical values in formula (1) the mobility is obtained: In the topological structure of the mono-mobile mechanism, with the "actuator mechanism" ) 1 , 0 ( MA , we remark one simple kinematic chain LD(2,3) type dyad and one complex kinematic chain LTt(4,5,6,7) type tetrad.
Therefore, the structural formula of the "motor mechanism" (MM) is: (2) The geometry of the mechanism is defined by the following parameters: 1) Fixed Cartesian coordinates:

The analytic calculation of the mechanism bar displacements
Due to the fact that the mobility of the wiper mechanism is equal to 1, there is a single independent parameter ( 1  ) for the calculation of the driven elements ( Then we deduce the scalar equations equivalent to the vector equation (3): Using the system consisting of the scalar equations ( 4) and ( 5), we calculate the angles φ2 and φ3 which are the positions of the coupler 2 and the rocker 3. Having φ3 , we obtain the position of the point C written by Cartesian coordinates: ) sin( ); cos( On the other hand, in the tetradic kinematic chain LTt(4,5,6,7) we identify two independent closed contours (figure 4).For each of these contours we write the vector equation of closing: From the two vector equations we dedude four scalar equations with four unknowns:  which are calculated from the system formed by the nonlinear scalar equations ( 9), (10), (11) and (12).

The calculation of the velocities and accelerations of the mechanism elements
In this stage of kinematic analysis, we impose the angle φ 1 , the constant angular velocity 30 /

   
  [1].We mention that the position angles φ 2 and φ 3 have been calculated at section 3.
For the velocity calculation, we derive with respect to time the two scalar equations of positions and we deduce the scalar equations of velocities: This system has two linear scalar equations with the unknowns 2  and 3   for which we deduce the formulas: For the open contours (4570) and (4670), we derive with respect to time the four scalar equations of positions (9,10,11,12) and we deduce the scalar equations of velocities: We notice that the terms from the right are known because they contain only the angular velocity 3   which has been previously calculated.Therefore, using this system we calculate the four angular velocities ., , , The acceleration calculation is performed by the derivation of the scalar equations of velocities ( 13) and ( 14) in which we consider .0 1 

 
For the contour (01230), the acceleration equations are: From this system consisting of the scalar equations ( 21) and ( 22), we calculate the angular accelerations 2   and 3   .For the contours (04570) and (04670), we derive with respect to time the four scalar equations of velocities (17, 18, 19, 20) and we deduce the scalar equations of accelerations.Then, using these equations we calculate the angular accelerations

The numerical calculation of the displacements, velocities and accelerations
For the numerical calculation of the nonlinear equations of displacements and for the linear equations of velocities and accelerations, we use the Mathcad ® software [11].
In this regard, we run the programming code file and we obtain the numerical values of the kinematic elements' lengths for the first chain LD(2,3) type dyad [1].
Then, for the second chain LTt(4,5,6,7) type tetrad, we obtain the charts for the angular displacements (figure 5).The kinematic charts allow us to perform the dynamic calculation of the mechanism which help us to predict the operation behavior.This can be done by means of calculation of all forces that influence the linkage movement such as inertial forces and moments, and reaction forces.

The modeling and kinematic simulation of the windshield wiper mechanism
In order to perform the modeling of all mechanism components, to assemble them and then to kinematically simulate the linkage we use the Inventor ® software which allows us to see the mechanism behavior during a kinematic cycle [13].
The virtual modeling begins with a planar prototyping of each component of the mechanism.After planar designing of the element layout, we create the third dimension (pad) of it and obtain the 3D component [1].
The assembly starts with the inserting of the fixed element (vehicle body) on which we mount one at a time the rest of the components.Thus, we obtain the mechanism assembly by means of the concentricity and off-set constraints imposed on each rotate joint (figure 9).

Figure 1 .
Figure 1.Kinematic scheme of the windshield wiper mechanism [1] the crank 1 is given by the angular displacement 1  , angular velocity 1  and angular acceleration 1  .The instantaneous position of each kinematic element (articulated bar) is deduced by means of the independent kinematic contour method (figure2).

Figure 2 .
Figure 2. The angular displacements of the kinematic elements

Figure 3 .
Figure 3.The vector contour of the kinematic chain 0 0 0 A ABB A

Figure 4 .
Figure 4.The tetradic chain with the two independent contours

Figure 6 .
Figure 6.The chart of the angular displacements for all kinematic elements

Figure 7 .
Figure 7.The chart of the angular velocities for the kinematic elements

Figure 8 .
Figure 8.The chart of the angular accelerations for the kinematic elements

Figure 9 .
Figure 9. Shot of the windshield wiper mechanism lengths of the kinematic bars: