# Rigging the Chebyshev Straight-Line Linkage Mechanism

I know its Four Bar Mechanism. While rotating I can't get desired results. Lets say the rest length is 1m. Please refer to the graphics for the details.

Chebyshev linkage

• I'm surprised there's no math instructions starting with the rotation of the upper (here green) connector. After all it is by this single angle that the state of the system can be described, no? And the description says the mechanism is supposed to convert rotational to linear motion, but in this specific configuration only the green element swings a full circle. And I know, it moves, so it's not very practical… I can get the sympy to calculate positions given a specific angle, but it fails at coming up with generalized equations (angle unknown)... pastebin.com/5fsKG6xv Commented Sep 28, 2023 at 19:52

## How to create a Chebyshev's linkage rig by switching the phase of an IK pole.

Use the IK structure shown below.

• Use the driver to rotate L2 bone between phi_min and phi_max according to the controller's rotation.
• Switch the IK pole angle of the L3 bone to 0 or 180 degrees using the driver according to the rotation angle of the controller.

• That's a really snappy solution.. not easy to find, IMO :) Commented Sep 27, 2023 at 6:37
• @Robin Betts, thanks. In fact, the first trick I came up with was to alternate the pole bone in two positions. Commented Sep 28, 2023 at 1:30