| Summary: | 碩士 === 國立成功大學 === 機械工程學系碩博士班 === 90 === Abstract
Parallel manipulators have been widely used recently, mainly due to their high stiffness structures. Parallel manipulators are suitable for applications requiring high accuracy under heavy loads. The computation of the Cartesian stiffness is essential in the stiffness control of a parallel manipulator. In practice, the compliance of a parallel manipulator is mainly contributed by the actuated joints. Therefore, the stiffness mapping from the joint stiffness to Cartesian stiffness is important.
The widely used formula of stiffness mapping was proposed by Salisbury in 1980. Recently, it was discovered that the work done in joint and Cartesian spaces is not conservative by using Salisbury’s formulation. A conservative congruence transformation (CCT) for serial manipulators has been proposed by Chen and Kao to correct Salisbury’s formulation.
Building upon the concept of CCT for serial manipulators, this thesis derives the formula for the stiffness mapping of parallel manipulators. We show that the proposed formulation obeys the law of conservation of energy by conducting numerical simulation for several planar and spatial parallel manipulators. The new formulation indicates that the change in geometry of a parallel manipulator due to compliance is captured by considering the differentiation of the Jacobian. This thesis also investigates the symmetry properties of parallel and serial manipulators.
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