The design, analysis, and control of active and passive compliant in-parallel manipulators

Catastrophe theory, which mathematically describes the phenomenon of jumps or discontinuities, is introduced in as simple a way as possible. It is very useful in analysis of compliant mechanisms. The theory states that most jumps which happen naturally belong to limited kinds of catastrophes (i.e., elementary catastrophe). Castrophe theory describes the effect of parameters changing to jumps. However, very complicated systems have not been solved by this method. One very important step in using this mathematical method is to find a potential-like function that describes the behaviors of the real world. For the compliant mechanisms, we defined system energy functions that describe the behaviors of spring systems.; The system energy functions for planar three-spring systems, including special cases and the more general case, and a spatial six-spring system, were derived. Catastrophe theory was applied to analyze these functions. The safe work-space for each compliant mechanism was graphically shown. Some detailed analysis of trajectory paths shows the stability changing of mechanisms. The procedure is effective in checking the behaviors of a mechanism, and the result is useful in modifying the original design to satisfy requirements.; A conceptual design and a procedure of parameter design of a spatial in-parallel manipulator are presented. The forward kinematics analysis gives a fortieth degree polynomial in a single variable. Each set of results is checked for satisfaction of the initial constraints. This means there may be up to forty different configurations. Static rigidity of this design is compared with some other widely used designs. The result shows that the octahedron in-parallel platform is a better design for general purpose application although some other design may be better for a specific application.; Two control criteria are presented for some redundant parallel manipulators. They may expand a manipulator's work-space or improve the static rigidity of a manipulator. The catastrophe analysis result is useful in determining the repeatability of a closure trajectory.