Parallel mechanisms represent a family of devices based on a closed kinematic architecture. This is in contrast to serial mechanisms, which are comprised of a chain-like series of joints and links in an open kinematic architecture. The closed architecture of parallel mechanisms offers certain benefits and disadvantages (stiffness versus dexterity, etc.). A particular subset of parallel mechanisms is known as Stewart platforms (or hexapods). The classic Stewart platform is based on a set of six independently actuated struts. The struts translate through sphere joints which reside on a stationary platform. Each strut terminates at a ball joint residing on a mobile tool platform. All joints allow passive rotation. The effect of this kinematic architecture is that the tool platform can be controlled to move in six axes. This report addresses some analytic approaches for modeling and characterizing these devices. These approaches cover inverse and forward kinematics, Jacobian evaluation, path execution, workspace envelope modeling, tool velocity characterization, and structural stiffness. A characterization is also made of a hybrid parallel-serial architecture consisting of a Stewart platform and a two-axis serial tool head. Numerical algorithms are also provided.

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