Inspiration for the creation of mechanical devices often comes from observing the natural structures and movements of living organisms. Understanding the wide use of modularity and compliance in nature may lead to the design of high-performance flexure systems or compliant devices. One of the most important nature-inspired paradigms for constructing flexure systems is based on the effective use of symmetry. With a rigid mathematical foundation called screw theory and Lie group. The research of this paper mainly focuses on: (i) Mathematical explanation or treatment of symmetry design wildly used in flexure systems, concerning with a series of topics such as the relationship between degree of freedom (DOF), constraint, overconstraint, decouple motion and symmetrical geometry, and How to guarantee the mobility unchanged when using symmetry design? (ii) A compliance-based analytical verification for demonstrating that the symmetry design can effectively improve accuracy and dynamic performances. (iii) The feasibility of improving accuracy performance by connecting symmetry design with the principle of elastic averaging. The whole content is organized around a case study, i.e. symmetrical design of 1-DOF translational flexure mechanisms. The results are intent to provide a rigid theoretical foundation and significant instruction for the symmetry design philosophy in flexure systems using kinematic principles.

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