Cam Synthesis

The kinematic analysis provided the required input angles of links 2 and 5 in the mechanism vector loop. These angles could be controlled by altering the height of the contact points of the links with the cam, denoted as E and F previously, relative to some fixed point. We chose to place this fixed point, which would serve as the center of our cam, 2.5 inches to the right and 2.5 inches below the origin of our coordinate system. This placed the center of the cam profile directly below the contact points with the links when the links were horizontal. The vertical offset was tuned to optimize the cam to a smoother shape while still keeping the cam size to a reasonable size for manufacturing. Kinematics were performed to find the height of point E using theta 2 and the height of point F from theta 5. This math involved two major assumptions. The first was that points contact points E and F were directly in line vertically with the fixed reference point of the cam, which is obviously not completely true; as the links rotate they obtain displacements in the horizontal direction which introduced some error. Additionally, the rotation of the links caused the contact points of links 2 and 5 with the cam to be read at slightly different times effectively introducing a slight phase error. However, these errors were negligible in magnitude and had minimal effect on the output image as was seen in the final demonstration. The heights above the fixed reference point formed a linear cam profile which can be seen in the figure below.

We learned  from our first prototype that linear cams had two significant problems: the linear cam profiles were often too jagged to be read effectively, and making smooth linear bearings and linear actuators is quite difficult to implement. We chose to convert the linear profile into rotational coordinates, which yielded the following cam profile.

 This cam profile provided a much smoother contour and allowed use of one rotational motor as the sole actuator into the system. The point cloud from this Matlab analysis was then imported into Solidworks as a spline and extruded to form a functional cam profile to feed into manufacturing systems. The final cam design in Solidworks is displayed below.

This file was ready to be fed into an automated manufacturing system. The completion of the cam design concluded the kinematic analysis and design portion of the project. The Matlab code used to perform all of the analysis described to this point is attached below.

Longhorn_Inversion_Code.m