Hybrid Connections of Simple Compliances

Achieving adequate force control is an important problem in the application of robotics technology to manufacturing tasks. This is particularly true for assembly tasks that require constrained interaction between a robotic manipulator and a workpart. One approach to this problem is the use of passive compliance. A number of methods have been proposed for designing a passive compliance mechanism with a prescribed spatial stiffness or compliance matrix using a parallel or serial connection of elastic devices. If the spatial stiffness or compliance matrix is isotropic, the constituent elastic devices are simple in the sense that they are strictly translational or rotational. Nonisotropic stiffness and compliance matrices require the use of elastic screw devices that couple translation and rotation. These screw devices are of a more complicated nature than the simple elastic devices that are sufficient for the isotropic case. In this article the authors demonstrate how these screw devices can be eliminated by using a hybrid connection of parallel and serial configurations consisting of only simple elastic devices to achieve any prescribed non-isotropic stiffness or compliance matrix. In particular, the authors show that an arbitrary spatial stiffness matrix can be realized using a parallel connection of no more than four simple serial mechanisms.