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In order to obtain a low-order array of parallel machine tools, each object in the multi-body system is first numbered. According to the object numbering method in the multi-body system, the machine bed is selected as the No. 1 object, and then in the direction away from the bed, according to the naturally growing sequence, the serial number of each object is sequentially determined, from one branch of the system to another branch. Until all objects have been calibrated.
Two coordinate systems are fixed on the object 2, which are the body reference coordinate system of the object 2 (the origin is O2) and the motion reference coordinate system G3 of the adjacent high-order body 3 of the object 2 (the origin is Q3), and Q3 is relative to the origin. The position of O2 is described by a vector q3 affixed to the object 2. The relative movement of the object 3 relative to the object 2 is described by a translation vector S3, and the rotation of the object 3 relative to the object 2 is described by a relative transformation matrix S23 between their body reference coordinate systems, and the relationship between the other adjacent bodies is This is similar. The tool holder is simultaneously connected to the simplified linkage so that the entire structure forms multiple closed loops at the tool holder. The ball joint joint is now unwound, and the original closed loop system is transformed into an open loop structure with four branches, and the open loop system is made consistent with the original closed loop system by an additional closed loop constraint equation.
Based on the multi-body system positioning model described above, it is considered that the absolute reference coordinate system of the parallel machine tool is set on the machine bed 1 and the motion reference coordinate system of each moving component may be inconsistent with the direction of the body reference coordinate system of the adjacent component. Then, the parallel machine tool motion position model POK=60t=uS1S(qV+SSGVsV)+S1KrPK is obtained. An expression is a general motion position model that calculates an arbitrary point on any part of a parallel machine tool.
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