A Unified Real-time Motion Generation Algorithm for Approximate Position Analysis of Planar N-Bar Mechanisms

This paper presents a novel real-time kinematic simulation algorithm for planar N-bar linkage mechanisms, both single- and multi-degree-of-freedom, comprising revolute and/or prismatic joints and actuators. A key feature of this algorithm is a reinterpretation technique that transforms prismatic elements into a combination of revolute joint and links. This gives rise to a unified system of geometric constraints and a general purpose solver which adapts to the complexity of the mechanism. The solver requires only two types of methods -- fast dyadic decomposition and relatively slower optimization-based -- to simulate all types of planar mechanisms. From an implementation point of view, this algorithm simplifies programming without requiring handling of different types of mechanisms. This versatile algorithm can handle serial, parallel, and hybrid planar mechanisms with varying degrees of freedom and joint types. Additionally, this paper presents an estimation of simulation time and structural complexity, shedding light on computational demands. Demonstrative examples showcase the practicality of this method.