Explicit dynamics formulation of Stewart-Gough platform: A Newton-Euler approach

Dynamic analysis of parallel manipulators plays a vital role in the design and control of such manipulators. Closed-chain kinematic structure affects the dynamics formulations by several constraints. Therefore, especially for higher degrees of freedom manipulators, manipulation of implicit and bulky dynamics formulation looses the tractability of the analysis. In this paper, a methodology and some simplification tools are introduced to achieve explicit dynamics formulation for parallel manipulators. This methodology is applied for the dynamics analysis of the most celebrated parallel manipulator, namely Stewart-Gough platform. By avoiding any recursive or component-wise derivations, the resulting dynamics formulation provides more insight for designers, and can be much easier used in any model-based control of such manipulators. In order to verify the resulting dynamics equations, Lagrange method is used to derive and compare the manipulator mass matrix. This methodology can be further used to formulate the explicit dynamics of other parallel manipulators.