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

本课题研究了单自由度和多自由度铅笔轨迹的运动学性质和综合方法。而线轨迹是其中跟踪元素跟随线的轨迹，在铅笔轨迹的情况下，线和线上点的位置都包括在内。因此，控制铅笔尖的运动和铅笔的方向是可行的。对于单个运动度，铅笔轨迹可视为直纹面上的点轨迹。需要控制铅笔的这类动作的典型应用包括钻孔、拧紧、焊接、切割、绘图以及激光或水射流定位。在设计和制造领域，这项研究的结果提供了线段的方向和位置的综合处理，消除了刚体运动的不必要约束。这使得铅笔轨迹综合和规划得到了相当大的简化。当自由度数受到限制以实现高速、高精度、易操作和低成本时，简化尤其有价值。*/

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.***//