Static equilibrium analysis of compliant mechanical systems using relative coordinates and loop closure equations

This paper deals with the static equilibrium formulation of mechanical systems, including rigid and compliant elements, and the determination of their final equilibrium configuration under known loads. Statically determinate as well as statically indeterminate systems are analysed. Relative coordinates are used as generalised coordinates. The system is modeled using homogeneous transformation matrices and loop closure equations. In the first phase of analysis (assembly), initial correct configuration of the system is obtained, from approximate input provided by the user. For the solution of the equilibrium problem, a potential function is used. Its minimisation, subject to rigid constraints yields the equilibrium configuration. The approach is implemented in a program and tested on a number of planar and spatial mechanical systems. The software program is intended to be used as a design aid for engineers.