Contributions to the synthesis of the windshield wiper mechanism with one rocker-slider blade

The paper deals with synthesis of the windshield wiper mechanism with one rocker-slider blade. Starting from the kinematic scheme of the constructive model designed by Mercedes-Benz motor vehicle company, a structure analysis on this complex mechanism consisting of three kinematic chains, of which two are articulated bar mechanisms and one is planetary mechanism, has been accomplished. The novelty of this paper consists in the presentation of an optimum synthesis method of the planar bar mechanism in two variants for the wiper blade driving. The first variant is a planar 4-bar mechanism type crank-rocker where the cosines theorem has been applied in order to obtain the lengths of the coupler and the crank. The second analyzed variant is a bi-contour linkage consisting of two 4-bar mechanisms linked in series. Further, the calculation of the planetary gear angular velocity on the complex mechanism with dyadic kinematic chains has been achieved. In order to do this, the immobilization of the planetary carrier method has been applied. Finally, the geometry of the driven linkage of the wiper mechanism type crank-slider which has two mobilities has been studied. A vector equation has been written in order to obtain the length of the variable blade.


Introduction
The windshield wiper mechanism special type analyzed in the paper had been developed by Mercedes-Benz ® in the 1980's [1].It consists of several bars, including a tetradic chain, and an annulus planetary gear which drive a rocker-slider blade (figure 1).with two "parallel" blades, which still the most used; -with two opposite blades, which are increasingly used.The mechanism with one rocker-slider blade is special due to the fact that motion of the blade is composed of both rotation and translation which makes it more efficient than the classical mentioned types, from the covered area point of view.

The topological structure and geometry of the windshield wiper mechanism
The kinematic scheme of the windshield wiper mechanism type Mercedes-Benz ® with complex structure consisting of articulated bars and an annulus planetary gear is presented (figure 2) [2,4].
The geometry of the kinematic scheme of the mechanism is defined by the following linear and angular parameters: The mobility of the mechanism is calculated by the formula [5]: where m is the mobility of the kinematic joint, Cm is the number of the kinematic joints of mobility m, r is the rank of the associated space, and Nr is the number of the closed contours of rank r.By analyzing the kinematic scheme (figure independent kinematic contours of the rank 3 (planar).By substituting these numerical values in formula (1) the mobility is obtained: The driving element 1 defines the "actuator mechanism" ) (2) We notice that the first dyadic chain LD (2,3) defines the first closed kinematic chain Lc(0,1,2,3) of type crank-rocker, and then the dyadic chain LC (4,5) defines Lc(0,3,4,5) of type rocker-rocker.
The third dyadic chain LD(6,e60) defines Lc(0,5,e60,6) where the bar e60 has the direction on the shared normal direction to the two tangent profiles in point H (figure 2).The fourth dyadic chain LD(7,8) defines Lc (5,6,7,8)  For each sub-mechanism (figure 3) the mobility is calculated by the formula (1): a) (angular displacement 10  ).The linking mechanism is consisting of the joint kinematic elements of the two neighbor mechanisms.The mobility of such linking mechanism is: (open kinematic chain 0, 5, 6); (kinematic chain 0, 5).We verify the mobility of the complex mechanism by means of the linking formula of the mechanisms: (3) By means of the two 4-bar sub-mechanism (figure 3c) we can obtain an oscillating rotation of the planetary carrier 5 by an obtuse angle  equal to circa 145°.This angle results from the condition that the wiper blade (fixed together to the slider 8) to cover 80% from the entire windshield surface.

The 4-bar planar mechanism type crank-rocker
The oscillating rotation movement by the obtuse angle of 145° can be obtained by means of the first analyzed variant of the planar articulated mechanism type crank-rocker (figure 4b) [2].
For the geometric synthesis of this mechanism we consider as known parameters: the base length ).In order to calculate the lengths 1 l and 2 l , the cosine theorem in the triangles ) ( From the two linear equations ( 4), the lengths for the coupler and the crank are resulting: The disadvantage of this solution (figure 4b) lies in the fact that the length of the crank 1 l results too big, and the transmitting angle in the extreme positions 1 D and 5 D , ) ( , is too small, under 20°.This is due to the geometry of the solution and it could cause the stall of the mechanism.

The 4-bar bi-contour planar mechanism
The second analyzed variant for the blade driving linkage is consisting of two 4-bar planar mechanisms linked in series (figure 5), of which the first is a crank-rocker mechanism (0, 1, 2, 3) and the second is a rocker-rocker mechanism (0, 3, 4, 5), that allows the multiplication of the oscillating rotation angle (from the angular displacement 3  to the imposed angular displacement 5  ) [2].This solution has been studied at section 2 from the mobility point of view.The geometric synthesis of the mechanism with two kinematic contours in series (figure 5) requires two stages: a) The design of the 4-bar mechanism type rocker-rocker (0, 3, 4, 5) on which, in order to obtain the rocker 5 rotation by the imposed angle 5  , the angle .We use the procedure applied in the case of the first variant of driving linkage (figure 4b), using the formulas (4), by imposing the angle 30  .We denote ) cos( 2; cos 2 From the two linear equations ( 7) the following solutions are obtained: In this case (figure 5) we notice that the length of the crank is smaller and the minimum transmitting angle 5  is maintained over the limit of 30° [5].

The angular velocity calculus of the planetary gear for the complex mechanism with dyadic kinematic chains
For the windshield wiper blade driving we consider the second variant with two dyadic chains (figure 6) on which the bar 5 is fixed together to the planetary carrier p(5) on which the planetary gear 6 is articulated.This gear 6 is geared with the annulus fixed gear 0 [2].We notice that in the initial position D0D1, the rocker 5 is positioned through the angle 50  with respect to the direction of the fixed articulations B0 and D0.
Together with the rocker 5 (having the angular velocity 5  ) the planetary carrier p(5) geometrically defined by the segment D0E articulated in E by the planetary gear 6 that has the angular velocity 6  .With respect to the point F1 (rotation instantaneous center), the planetary gear 6 is rolling inside on the dividing circle of the fixed annulus gear 0.
For the calculation of the angular velocity 6  of the planetary gear 6, we apply the immobilization method of the planetary carrier p(5), resulting the following ratio:

The geometry of the driven mechanism type crank-slider
The driven mechanism is type crank-slider with wiper blade (figure 7) and it represents the third kinematic chain in the configuration of the complex windshield wiper mechanism with bars and gears (figure 2) [2].Point M (the end of the wiper blade) executes a rotation with respect to the fixed articulation D0 (figure 7) simultaneously with a sliding movement in respect of bar 5 through the rotation of the crank 6 with respect to the mobile articulation E.
Basically, the segment GM represents the wiper blade which is fixed together with the slider 8, performing a rotate-sliding movement on the windshield surface.The bar 5 is a rocker with the fixed articulation D0 (figure 7a) being positioned by the angle φ50 .The crank-slider mechanism geometry is defined by constant and variable parameters of the vector contour EFG (figure 8b).
The rotation angle of the crank 6 (fixed together with the planetary gear 6) is obtained by means of the formula (14): We choose the mobile coordinate system

Conclusions
The windshield wiper mechanisms are safety and comfort systems on any vehicle.These spatial mechanisms are assimilated as planar linkages with articulated bars situated in parallel planes.The advantage of the windshield wiper mechanism with one rocker-slider blade is that it covers the wiping surface with 20% higher than the classical mechanism with two parallel blades.However, the disadvantage of it is the decreased speed due to use only one blade.
Only two of four studied solutions for the driving linkages of this wiper mechanism have been highlighted: one 4-bar mechanism type crank-rocker and two 4-bar mechanisms linked in series type crank-rocker and rocker-rocker.The other two solutions that have been studied in another paper are: mechanism with a triadic chain and mechanism with a tetradic chain.

Figure 1 .
Figure 1.The windshield wiper mechanism with one rocker-slider blade Two types of windshield wiper mechanisms are the most used on present automobiles:

Figure 3 .
in which there are four planar articulations ) joint(8,5).The point M belongs to the slider 8 which translates with respect to the bar 5 that executes an oscillating rotation with respect to the fixed point 0 D .The three sub-mechanisms (independent kinematic chains): crank-slider with oscillating guide (a), annulus planetary gear (b) and two 4-bar chained linkages (crank-rocker and rocker-rocker) (c)

Figure 4 . 5 D
Figure 4. a) The discrete positions of the wiper blade on the windshield; b) The 4-bar mechanism type crank-rocker for the angle  displacement achieving

Figure 5 .
Figure 5.The kinematic scheme regarding the optimum synthesis of the articulated mechanism in the second variant with two dyadic chains design of the 4-bar mechanism type crank-rocker (0, 1, 2, 3) through choosing the length 3 l choose the position of the fixed articulation 0A taking account the condition that the transmitting angle to be at least the minimum

Figure 6 .
Figure 6.Kinematic scheme of the windshield wiper mechanism in two positions

Figure 7 .
Figure 7. Kinematic scheme of the bi-mobile driven mechanism

5 5Figure 8 .
Figure 8. Kinematic scheme of the crank-slider mechanism (a) with the vector contour (b)