Instantaneous Pencil-Trajectories of Single and Multiple Degree-of-Freedom Linkages and Manipulators

单重和多重的运动学性质和综合 度的自由铅笔轨迹进行了研究，在这 研究项目。而直线轨迹是指 在铅笔的情况下，跟踪元素跟随一条线 轨迹，包括直线和直线上一点的位置 包括在内。因此，可以控制 铅笔的尖端和铅笔的方向。用于 单个运动度的铅笔轨迹可以被认为是 直纹曲面上的点轨迹。典型应用如 需要控制铅笔的运动包括钻孔，拧动， 焊接、切割、拉伸和激光或水射流定位。在 设计和制造领域，从这项研究的结果 提供一个综合治疗的方向和 线段的位置，从而消除不必要的 刚体运动的约束。这导致了一个相当大的 用于铅笔轨迹合成和规划的简化。 当数量减少时，这种简化特别有价值。 自由度是有限的，以实现高速，高 精度高，操作简单，成本低。*//

The kinematic properties and synthesis of single and multiple degrees-of-freedom pencil trajectories are investigated in this research project. Whereas a line trajectory is one in which the tracing element follows a line, in the case of a pencil trajectory, both the line and the position of a point on the line are included. It is therefore feasible to control the movement of the tip of the pencil and the orientation of the pencil. For a single degree-of-motion a pencil trajectory may be regarded as a point trajectory on a ruled surface. Typical applications of such motions requiring control of a pencil include drilling, screwing, welding, cutting, drawing, and laser or water jet positioning. In the area of design and manufacturing, results from this research provide an integrated treatment of both the direction and position of a line segment, there by eliminating the unnecessary constraint of a rigid body motion. This leads to a considerable simplification for the pencil trajectory synthesis and planning. The simplification is especially valuable when the number of degrees of freedom is limited to achieve high speed, high precision, easy of operation, and low cost.***//