Study on dynamic isotropy of a class of symmetric spatial parallel mechanisms with actuation redundancy

In this paper, we study dynamic isotropy using natural frequency analysis for a class of symmetric spatial parallel mechanisms (SSPMs) with 2p (p≥3) struts. This kind of dynamic isotropy has been defined as the square roots of the eigenvalues of the equivalent mass-spring systems formed via the interactions between rigid-body mechanical systems and their driving systems. Analytic expressions for these eigenvalues are then derived in the task space, which is linearly dependent on p. Furthermore, a general compliance center was found for all the SSPMs in which the parallel mechanisms are fully decoupled. Based on the dynamically decoupling, then, dynamic isotropy for the SSPM is discussed which shows that though taking the inertial parameters into consideration, the SSPM can not attain complete dynamic isotropy and the optimal dynamic isotropy index is the quartic root of two. At the end of the paper, to demonstrate these results, an example is given.