远中心柔顺机构弹性单元刚度建模研究

Research on Stiffness Modeling of Elastic Element in RCC

为得到远中心柔顺机构(RCC)中常用的金属梁单元、层叠弹性单元(ESP)的刚度性能,在材料力学四个基本假设下,根据弹性变形原理,对单元末端建立金属梁刚度矩阵,并通过伴随变换进行解耦,得到其对角形式。对端部具铰链梁单元、U副梁单元、球关节梁等不同运动副的单元进行刚度建模,给出铰链处的刚度矩阵,发现转动副处的刚度矩阵无法解耦,而U副和球副可解耦。建立了ESP弹性单元的刚度模型,发现在一端固定条件下,末端自由、添加U副和添加球副均利于形成RCC机构的解耦刚度性能。研究为RCC机构的设计提供了参考。

To obtain the stiffness performance of the metal beam element and elastomer shear pad(ESP)element in common use in the remote center compliance(RCC),the stiffness matrices were built according to the principle of elastic deformation and four basic hypothesis in the theory of material mechanics.The stiffness matrices were built at the end of each element and decoupled through adjoint transformation and the block-diagonal form were finally obtained.The stiffness models of the elastic element with different joints at the end were also built and stiffness matrices for the location of joints were given.It is found that stiffness matrices of universal joint and spherical joint can be decoupled,while revolute joint can not.Therefore,when the two kinds of elastic elements are fixed at one end,the decoupling stiffness performance for RCC can be achieved with no joint,universal joint and spherical joint at the other end.The research offers a reference to the design of RCC.