Analysis of the Robot Main Body

Position Analysis

Mainly a mathematical problem:

I first decide a spatially fixed direction γ (doesn't change even if cam rotates) and a fixed distance d as well.

Together both of these define the position of a desired point that lies on the cam's plane.

The cam is tilted at 20 degrees about the X axis, and the shaft rotation is represented by rotation about the Z axis.

The purpose of this definition is because the red link base, represented by the dashed line, its corner is always spatially at γ = 45 degrees and the other at γ = 135 degrees, and they follows closely to the points of the cam at γ with distance d.

What I ultimately will do is analyze the motion of one of the corner and see how it moves in the XZ plane. This motion will represent how the red link rotate.

Assumption that I make for this analysis: the base never moves vertically, the corner exactly touches the circumference at that direction, so I use that as the fixed distance.

For one of the corner:

γ = 45 degrees.

d:

For my case, radius of the circle was 20 mm and eccentricity b was 10 mm. thus d = 11.6372.

The steps to follow now to get the motion of the corner of the red link base after the shaft has rotated θ angle:

If we rotate the cam about Z axis for θ, the cam follower will follow the position of the point at -θ angle. Thus set the new γ = previous γ - θ.
Get the vector that represents the point that represents the corner:
Premultiply it by a rotation matrix that represents rotation about X axis for 20 degrees. (Due to cam tilted by 20 degrees)
Premultiply it by another rotation matrix that represents rotation about Z axis for θ degrees.

Results: (These two points are the motion at γ = 45 and γ = 135. Between each frame the shaft has rotated an additional 10 degrees.

The line between them represents the orientation of the red link base. My result is consistent with what we have seen from the model: fast motion in the middle, and slow when reaching the limits.

Velocity Magnitude: