Four bar linkage forward kinematics question

Hi, this is my first post on this forum.

I have a design for a machine with two mutually perpendicular revolute joints, i.e.

a base,

a hinged joint,

an arm,

a hinge perpendicular to the first joint,

second arm.

Using D-H forward kinematics I've got code working using 4*4 transformation matrices.

Now, there's a proposal to change one of the revolute joints to a 4-bar linkage.
All the joints in the new linkage will be parallel to the original axis.

(ASCII art attempt:)

(+ = joint)



---/ ---------\

This means the simple revolute joint must be replaced by four
offset parallel revolute joints, which form a closed loop.

The simplicity of the original arrangement meant it was quite straightforward
to do the kinematics. The proposed arrangement has me confused.

So, I _think_ I need to replace the simple 4*4 matrix describing a revolute joint,
with a matrix describing the 4-bar linkage.

The treatments I've found are too general for me to figure it out.

Can anyone out there help me? How do I derive the new matrix?
Or is there a better approach?

Last edited:

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