Automatic Synthesis of a Planar Linkage Mechanism With Revolute Joints by Using Spring-Connected Rigid Block Models

Abstract

In traditional linkage design practice, a designer first decides the specific linkage type, such as a four- or six-bar linkage, and then varies the joint locations and link lengths until the designer finds the desired linkage. The objective of this research is to establish an automatic mechanism synthesis method that determines the linkage type and dimensions during the synthesis process. The synthesis process can be formulated as a minimization problem. However, the process can be extremely difficult and time-consuming unless there is a single unified linkage model that represents any linkage mechanism without complicating kinematic analysis and allows the use of an efficient gradient-based optimizer. The main contribution of this investigation is to propose a unified planar linkage model consisting of rigid blocks connected by zero-length springs having real-valued variable stiffness. Stiffness controlling variables are the design variable of the minimization problem and a general planar linkage can be simulated by the spring-connected rigid block model if the stiffness value is chosen appropriately. Though mechanisms involving only revolute joints are investigated and the solved problems are relatively simple, the notion of the block model and the synthesis formulation in real variables are expected to give a different perspective on mechanism synthesis.