2.3 Determination of tool pose conditions
With the concept of the cutting face of the tool, the creation process of the machined surface on the machine tool can be described as creating a machined surface by moving or rotating the cutting face of the tool relative to the surface being machined. In this process, the tool must be in contact with the surface to be machined without interference, that is, satisfy certain contact conditions and interference conditions, so that there is a certain position and posture between the tool (O P ) and the workpiece (O W ). It is required that this relative relationship can be described by the tool's pose matrix [ W T P ].
The contact condition between the cutting surface and the surface to be machined is that the O C coordinate system coincides with the O S coordinate system, thereby deriving the position and orientation matrix of the tool relative to the workpiece:
[ W T P ]=[ W T S ] . [T PC ] -1 (3)
It can be seen from the above formula: [ W T P ] contains information about the tool and the workpiece. [ W T P ] is a condition that should be met during the creation of a machine tool. D. Perform the necessary interference check on the tool pose matrix obtained above, and mainly check whether other points on the blade interfere with the machined surface. If no interference occurs, the requested tool pose matrix is ​​feasible.
3 Design method of machine tool motion function scheme
With the pose matrix of the tool, the problem that needs to be solved now is how to determine the number, sorting, etc. of the necessary motion units between the tool and the workpiece in the machining process by [ W T P ]. This paper mainly studies the design of the motion function of tandem machine tools. We use the motion cascade matrix [T WP ] between O P and O W to achieve [ W T P ] (as shown in Figure 3).
[T WP ]=[ W T P ] (4)
Fig. 3 Relationship between tool pose matrix and motion cascade matrix
By solving the above formula, the motion function of the machine tool can be obtained. Each motion unit arrangement in [T WP ] represents a motion scheme. This is a multi-solution inverse kinematics problem, and it is very difficult to solve it directly. Based on the characteristics of tandem motion and the creation principle of the machined surface, a hierarchical analytical method is presented. If the surface to be processed is S(u, v), it is a bus when v=const, and a wire when u=const. The resolution steps are as follows:
(1) determining the bus bars and wires of the surface to be processed;
(2) Analysis of the motion function when creating a processing bus:
Determine the tool pose matrix [ W T P ]u when the bus is created, and set the motion cascade matrix [T WP ]u according to the characteristics of [ W T P ]u, and make
[T WP ]u=[ W T P ]u (5)
Solving equation (5), if the solved motion unit is a function of u, it indicates that the motion unit is necessary, otherwise the set motion unit is redundant. This makes it possible to determine the motion unit required to create the busbar.
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