Precision of Rotation Analysis of Two-axis Rectangular Cross-section Corner-filleted Flexure Hinges

Abstract

A two–axis rectangular cross–section corner–filleted flexure hinge as an alternative to the conventional flexure hinges for 3D multi–degrees of freedom compliant mechanisms is presented. The 3D mechanical model of two–axis flexure hinge is established,and the precision of rotation of the flexure hinge is developed on the basis of Castigliano's theorem. The closed–form formulas for the flexure hinge are obtained by the method of substitution. Aiming at errors arising from rotation center deviation of the flexure hinge,the results show that compared with analytical model and the finite element simulation,the error margins are within 7%. It is prove that the analytical model is accurate. Finally,the influence of the structural parameters on the precision of rotation of the flexure hinge is analyzed,and it is concluded that the precision is proportional to the Young's modulus or the shear modulus of the material. When the minimum thickness δ and the minimum width b of the flexure hinge are defined,whether the precision of rotation of the flexure hinge reduces or improves depending on the increment or decrement of the radius R or the beam length l. But the influence of the beam length l is more obvious. When the radius R and the beam length l of the flexure hinge are defined,whether the precision of rotation of the flexure hinge is improved or reduced depends on the increment or decrement of the minimum thickness δ or the minimum width b. Some theoretical principles for engineering design of flexure hinges are provided from the above conclusions.