Kinematic Analysis and Synthesis - Group 10

Our kinematic analysis focused on deriving geometry for our follower mechanism and cams. Analysis was done with hand calculations and MATLAB with additional verification performed in Solidworks. 

In order to decide on the geometry of the slider crank mechanism, we first calculated the required range of motion of the end effector to reach the ‘H’, ‘E’, ‘L’, ‘O’, and ‘Enter’ keys by physically measuring the size of our chosen keyboard. We then decided on a maximum range of motion for our sliders based on the length of steel shafts we had access to. We then created a representation of the mechanism in a Solidworks sketch and plotted the coordinate points of the center of each of the keys of interest on a keyboard by measuring their position on our final keyboard as can be seen below.

We were primarily concerned with the horizontal mobility of our mechanism as the keyboard is relatively long in the horizontal direction. We quickly developed some useful metrics that helped us finalize our geometry. First, we found that reducing the distance between the input sliders increased the range of motion of the end effector. Furthermore, increasing the distance between the end effector and the link it was attached to increase the range of motion of the end effector as well as making small changes in the angle of the link have a larger effect on the final position. Finally, shortening the crank link increased the range of motion as small differences in the positions of the sliders produced a large change in the angle of the end effector’s link. Using these metrics in combination with our design parameters, we decided on the geometry pictured below.

In order to perform our position analysis, we treated the crank slider base as a datum and considered the relative position between the slider and crank base. We then used hand calculations to establish a relationship between the angle of the link attached to the end effector and the relative position of the sliders. 

However, the final equation gave the angle of the end effector link as a function of the relative position so I would need to obtain the inverse of this equation in order to calculate the end effector position based on the relative position of the sliders. Since the inverse could not be determined analytically, we obtained a relationship between the two variables by plotting the full range of the angle of the end effector link and obtaining the corresponding relative position of the sliders. We then used Matlab to reverse-lookup values for the link angle given a relative position. We then calculated the final position of the end effector given the relative position of the sliders by adding vectors representing each link starting from our datum to our end effector.

In order to confirm the accuracy of our calculations, we recreated the geometry of the mechanism in Solidworks and plotted verification points to confirm the equations we calculated were accurate as shown below.

In order to obtain the final slider positions, we took the coordinates for each of our target keys and used the calculations discussed above to find the relative position of sliders that would produce the same x coordinate. We then moved our datum point to match the y coordinate of the end effector to the key location.

Our analysis code and hand calculations are included in the appendix.