Optimal design techniques for kinematic couplings

Kinematic couplings are well known to the precision engineering community as simple devices that provide rigid, repeatable connection between two objects through usually six local contact areas. They serve many applications that require 1) separation and repeatable engagement, and/or 2) minimum influence that an imprecise or unstable foundation has on the stability of a precision component. Typically, the coupling design process starts by arranging or adapting one of two classic configurations, the three-vee coupling or the tetrahedron-vee-flat coupling, to suit the geometry of the application. It is often sufficient to analyze only the contact stresses and perhaps the coupling stiffness when the configuration remains fairly conventional (i.e., planar) and the application is not particularly demanding. Otherwise, effort spent optimizing the configuration through additional analysis and/or testing is well worthwhile. This paper proposes several optimization criteria and presents analysis techniques for optimizing kinematic coupling designs. The general modeling approach uses [6 × 6] transformation matrices to reflect contact stiffness matrices to a common coordinate system where they are added together as a parallel combination, for example. This method has wider applications particularly for flexure systems, which will be the subject of a future article. In addition, the reader may find the kinematic coupling designs presented in this paper useful for future applications.