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Abstract This paper presents a novel real-time kinematic simulation algorithm for planar N-bar linkage mechanisms, both single- and multi-degrees-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.
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This content will become publicly available on April 1, 2026
Point-Based Models: A Unified Approach for Geometric Constraint Analysis of Planar n -Bar Mechanisms With Rotary, Sliding, and Rolling Joints
Abstract 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.
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- Award ID(s):
- 2126882
- PAR ID:
- 10635248
- Publisher / Repository:
- ASME
- Date Published:
- Journal Name:
- Journal of Mechanisms and Robotics
- Volume:
- 17
- Issue:
- 4
- ISSN:
- 1942-4302
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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