Autonomous Synthesis of Mechanisms With Obstacle Avoidance Using the Spring-Connected Rigid Block Model

Abstract

Mechanisms that transform simple rotational motion into desired motions are essential for robots and automobiles. Designing such mechanisms without any baseline is challenging because it requires determining both the topology and dimensions of link-joint connections. To address this issue, computationally efficient gradient-based synthesis methods using ground bar or block models have been developed to automatically determine both topology and dimensions. However, existing methods do not consider obstacle avoidance, limiting their applications. Obstacle avoidance is critical for reliable operation, preventing collisions with other components and ensuring efficient use of space. If revolute joints are relocated to avoid their intrusions, the mechanism will not function as planned. In this research, we propose a novel gradient-based method that incorporates obstacle avoidance into the automatic design of planar mechanisms. Our approach is to introduce a new obstacle avoidance constraint function in the spring-connected rigid-block-based formulation. The developed function assesses whether the revolute joints formed during optimization collide with obstacles. This enables the synthesis of mechanisms that adjust their topology and dimensions to avoid obstacles using a gradient-based optimization formulation, ensuring that revolute joints are placed away from obstacles. We demonstrate the effectiveness of our method with examples involving circular and rectangular obstacles. These results show that our approach produces mechanisms with adjusted topologies and dimensions that avoid collisions while the synthesized mechanisms generate the desired paths. Our research expands the practical applicability of the automated mechanism design, laying the groundwork for synthesizing a wide range of mechanisms.