Some practical examples of planar (ref), spherical (ref) and spatial (ref) mechanisms can be seen below.
We use two different gradient based approaches to simulate one degree of freedom closed loop mechanisms. The approach can handle both revolute and prismatic joints.
In first approach, we club all the rigidity constraints into a single cost function. When the system is perturbed due to input, the cost function is minimized to find unknown coordinates. If the cost value does not converge to zero, a feasible solution cannot be found.
In this approach, we handle each rigidity constraint seperately as a non-linear polynomial constraint. A jacobian matrix for this system of equation can be found and a numerical solution can be found iteratively using Newton-Rhapson algorithm.
Two planar mechanisms are simulated. First is the Theo-Jansen walking-robot mechanism which uses an eignt-bar mechanism. The second is Watt's Steam Engine mechanism which brought around the industrial revolution.
Two spherical mechanisms are simulated. The first is a simple four bar mechanism with revolute joints. The second is a six bar Watt-I mechanism with one of the fixed pivots being prismatic.
A spatial 5-SS platform mechanism has been simulated.
If you find the code, models, or data useful, please cite this paper:
@inproceedings{Sharma2019simulation,
author = {Sharma, Shashank and Purwar, Anurag},
title = "{Using a Point-Line-Plane Representation for Unified Simulation of Planar and Spherical Mechanisms}",
volume = {Volume 5A: 43rd Mechanisms and Robotics Conference},
series = {ASME International Design Engineering Technical Conferences and Computers and Information in Engineering Conference},
year = {2019},
month = {08},
doi = {10.1115/DETC2019-98194},
url = {https://doi.org/10.1115/DETC2019-98194},
}