Integrated optimization synthesis of linkage mechanism structures and dimensions free from kinematic defects

Abstract

This paper presents a novel methodology for the integrated optimization synthesis of linkage mechanism structures and dimensions, utilizing a kinematic defect-free dyad comprising two bars with three revolute joints (3R dyad). The approach overcomes the challenges associated with designing single structure linkages, kinematic defects, and optimization issues common in traditional multi-bar mechanisms. By standardizing the parameterization of defect-free 3R dyads, this methodology facilitates the uniform mapping of structural and dimensional parameters into a consolidated design variable space, enabling simultaneous optimization of topological structures and dimensions—a significant advancement over traditional methods that address these aspects separately. Moreover, the proposed method fundamentally prevents kinematic defects by ensuring that all generated mechanisms inherently satisfy kinematic constraints throughout the optimization process, thereby eliminating the need for defect screening during or after optimization. The synthesis method for linkage structures, based on the 3R dyad and its unified dimension parameterization strategy, is detailed. To substantiate the proposed methodology, experimental tests were conducted on two six-bar mechanisms for path generation tasks and two eight-bar mechanisms for rigid-body guidance tasks. The outcomes confirm that the optimized linkage mechanisms precisely fulfill diverse motion requirements without kinematic defects. Additionally, the optimization design of a six-bar leg rehabilitation mechanism demonstrates the practicality and efficiency of this approach, further validating its superiority in real-world applications.