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Deficiencies are existed for currently formulas of mobility calculation for planar mechanism. They are not suitable for planar mechanism with virtual constraints and the number of general constraints equal to 4. To solve the problem, the new concepts of virtual loop, virtual-loop constraint and virtual pair are defined to establish a general f ormula for DOF of planar mechanism; the calculation method for virtual-loop constraint and the mobility of link-group are also given. It is proved that the new formula is correct, general, simple and effective through the mobility analysis of several different kinds of planar mechanisms.

In view of the special characteristics of cams grinding, some key technologies of grinding force adaptive control system are researched, including selection of inspecting parameter, modeling of grinding feed system, and design of controller. Results of simulation indicate that this system can ensure circular grinding force steady and enhance the machining quality of cams when the grinding allowance is of variety.

A basic method and characteristic of tool’s radial offset for conical enveloping surface, its structure and working theory as well as the most advanced planetary grinding head used in tool’s radial offset in the world are introduced. In order to improve the dynamic property of grinding head and method used in tool’s offset in existence, a new type of grinding head that can realize tool’s radial offset to big tool’s radial error was developed. It has the advantages of simpler structure, easier machining, lower cost, continuous and stable machining, and high efficiency, and is a new method of complex tool’s position offset.

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