Conceptual Designer Mechanisms: Chebyshev’s Plantigrade Machine

SOLIDWORKS Conceptual Designer is a useful 3D modeling app on the 3DEXPERIENCE platform. It allows you to create and animate 3D parts. Over the past few weeks, I have been creating various mechanisms of multiple levels of difficulty with it and creating the animations of the mechanisms in motion. This blog series will display the mechanisms that I created and explain the steps I took to make them.

The first mechanism I’ll show you is Chebyshev’s Plantigrade Machine, which demonstrates how to convert rotary motion to walking motion. This linkage was created by Russian mathematician Pafnuty Chebyshev. The motion of the machine is meant to display the same form as that of plantigrade walking animals, such as bears, rabbits, and, sometimes, humans. Plantigrade’s machine has four “legs” that create a semi-circular pattern and, as expected, look like an animal walking.

Stage 1 (Left Half): To make the plantigrade machine easier to make, I used a series of links at 0.25” thickness and different lengths that gave the machine a unified appearance. These were created by making a sketch, using the centerline slot to make the link at 1-inch width and varying lengths. To get the mechanism to make the proper motion pattern, the links had to be made with Chebyshev’s proportions. I set the length of the crank to be 2-inches and had that as A. The machine’s rocker was 2A away, or 4-inches. Its length is 2.5A or 5-inches, and is at the end of the long beam I made to connect both sets of cranks and rockers. I made a leg that was 5A or 10-inches long and pinned one end to the end of the crank and the middle to the end of the rocker. I repeated these steps for the other side of the main beam, setting the two cranks parallel.

Stage 2 (Right Half): The right half of the machine is a close copy of the left half. The cranks for this half are parallel to those of the other half, and the rockers are mostly in line with their counterparts on the other side. When animated, the semi-circular pattern traced by the ends of the legs becomes evident, and the plantigrade motion is shown.