Type synthesis of reconfigurable single-loop mechanisms based on planar rhombus mechanisms

This paper deals with the type synthesis of reconfigurable single-loop mechanisms (RSLMs) using screw theory. A novel approach is proposed to synthesize RSLMs by inserting two or four revolute joints to a planar rhombus 4R mechanism. Using the proposed approach, four types of wrench systems of RSLMs are obtained. The reconfiguration analysis of an RSLM with a constraint force system is then carried out using the kinematics close-loop equation and screw theory method. By locking the R joints, it can be found that the mechanism can realize a 1-DOF planar 4R mode, a 1-DOF Bricard mode, a 2-DOF serial mode, a 1-DOF coaxial mode, a 1-DOF Bennett mode, and a 2-DOF spatial 8R mode. Furthermore, four transition configurations among different modes are identified. To verify motion modes of the mechanisms, serval 3D printed models are also presented. This work provides a framework for further study of type synthesis reconfigurable mechanisms from overconstrained single-loop mechanisms.