Abstract
The advent of spatial parallel mechanisms means that the primary considerations of designers are the degree of freedom of the end effector and its actuations. It is urgently necessary to differentiate the degree of freedom of the end effector from the independent number of actuations to completely control the end effector under any configurations. By uniformly depicting the kinematic and geometry constraints of mechanism in one Cartesian coordinate system, this chapter discusses a system method that should be widely used to study the degree of freedom of spatial parallel mechanisms with an end effector. For complex spatial mechanisms, the kinematic chains of the specified end effector might not be pure series which often contain sub-parallel chains; the twists of the sub-parallel chains can be equivalently substituted with the method discussed in Section 4.4 of Chapter 4. Therefore, this method can be used to analyze and synthesize the complex spatial mechanisms.
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