This paper focused on the corner-filleted flexure hinge to investigate its compliance matrix.First,based on the beam theory,an analytical equation of corner-filleted flexure hinge's planar deformations
were obtained,and the closed-form planar compliance matrix equation was obtained,the simple calculation equation of compliance matrix was also reduced when rt r is the radio of the hinge,t is the thickness of the hinge.Then,finite element model of the corner-filleted flexure hinge was established,the analytical results and finite element results of the compliant matrix were obtained when changing the radio of r/t and l/t(l is the length of the hinge),and the relative errors between the analytical and finite element data were calculated.The results indicate that when the ratio of l/t≥4,the analytical data error will be less than 5.5%,and when the ratio of 0.1≤r/t≤0.5,the analytical data error will be less than 9%,especially when 0.2≤r/t≤0.3,the error will less than 6.5%;when r/t≤0.3 and r/t≤0.2 the simple analytical data error will be less than 9% and 7% separately.Finite element simulation results confirm the theoretical formulation data.The above closed-form compliance matrix equation will be useful for the design and optimization of flexure hinges and compliant mechanisms.
