Point-Based Models: A Unified Approach for Geometric Constraint Analysis of Planar n-Bar Mechanisms with Rotary, Sliding, and Rolling Joints

Kinematic simulation of planar n-bar mechanisms has been an intense topic of study for several decades now. However, a large majority of efforts have focused on position analysis of such mechanisms with limited links and joint types. This article presents a novel, unified approach to the analysis of geometric constraints of planar n-bar mechanisms with revolute joint (R-joint), prismatic joint (P-joint), and rolling joint. This work is motivated by a need to create and program a system of constraint equations that deal with different types of joints in a unified way. A key feature of this work is that the rolling joint constraints are represented by four-point models, which enables us to use the well-established undirected graph rigidity analysis algorithms. As a result, mechanisms with an arbitrary combination of revolute-, prismatic joints, and wheel/gear/wheel-belt chains without any limitations on their actuation scheme can be analyzed and simulated efficiently for potential implementation in interactive computer software and large-scale data generation.