Dynamic equations of chain structured robotic manipulators with compliant links and joints are developed in a non-recursive symbolic form. A program is developed in REDUCE to automate the symbolic expansion of these equations for any given chain structured manipulator. The symbolic non-recursive form of dynamic model is particularly suitable for controller synthesis and real-time control implementations. The link flexibility is included in the formulation using assumed mode shapes. The mode shapes and the parameters that are functions of the mode shapes are kept in symbolic form so that once a symbolic model is generated, different types of mode shapes can be studied using the same model. Because of the structural similarity between the developed equations and the well known rigid manipulator equations, the computer automated symbolic expansion capability presented here are likely to be utilized widely by many other researchers in the area who are already familiar with rigid manipulator problems.
