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首页> 外文期刊>Proceedings of the Institution of Mechanical Engineers. Part K, Journal of Multi-body Dynamics >Effect of the coordinate frame on high-order expansion of serial-chain displacement
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Effect of the coordinate frame on high-order expansion of serial-chain displacement

机译：坐标系对连续链位移高阶扩展的影响

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An algorithmic differentiation technique gives a simpler, faster power series expansion of the finite displacement of a closed-loop linkage. It accomplishes this by using a higher order than what has been implemented by complicated prior formulas for kinematic derivatives. In this expansion, the joint rates and axis lines generate the instantaneous screw of each link. Constraining the terminal link to have a zero instantaneous screw satisfies closure. In order to maintain closure over a finite displacement, it is necessary to track the spatial trajectory of each joint axis line, which in turn is directed by the instantaneous screw of a link to which it is attached. Prior algorithms express these screws in a common ground-referenced coordinate frame. Motivated by the kinematics solver portion of the recursive Newton-Euler algorithm, an alternative formulation uses sparse matrices to update the instantaneous screw between successive link-local frames. The recursive Newton-Euler algorithm, however, conducts the expansion to only second order, where this paper shows local coordinate frames that are only instantaneously aligned with their respective links give identical expressions to those in frames that move with the links. Moving frames, however, require about 40% of the operations of the global-frame formulation in the asymptotic limit. Both incrementally translated (Java) and statically compiled (C++) software implementations offer more modest performance gains; execution profiling shows reasons in order of importance (1) balance of calculation tasks when below the asymptotic limit, (2) Java array bounds checking, and (3) hardware acceleration of loops.
机译：算法微分技术使闭环连杆的有限位移的幂级数展开更简单，更快。它通过使用比复杂的运动学方程式更高的阶数来实现。在这种扩展中，连接速率和轴线产生每个连杆的瞬时螺钉。将接线端子约束为具有零瞬时螺钉即可满足闭合要求。为了在有限的位移上保持闭合，必须跟踪每个关节轴线的空间轨迹，而该关节轨迹又由连接它的链节的瞬时螺钉引导。先前的算法在共同的地面参考坐标系中表达这些螺钉。受递归Newton-Euler算法的运动学求解器部分的激励，一种替代公式使用稀疏矩阵来更新连续链接局部帧之间的瞬时螺丝。但是，递归Newton-Euler算法仅将扩展进行到二阶，其中本文显示了仅与它们各自的链接瞬时对齐的局部坐标系给出了与随链接运动的框架中相同的表达式。但是，移动框架在渐近极限中需要全局框架公式的大约40％的运算。增量翻译（Java）和静态编译（C ++）软件实现都提供了更为适度的性能提升。执行性能分析按重要性顺序显示原因：（1）低于渐近极限时的计算任务平衡；（2）Java数组边界检查；（3）循环的硬件加速。

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