????????Pieper准则是Pieper.D.L于1968年在其论文“THE KINEMATICS OF MANIPULATORS UNDER COMPUTER CONTROL”中提出的用于判别机械臂逆运动学问题是否存有封闭解的准则，是存在封闭逆解的充分条件，具体内容为：
????????当如下条件之一满足时，一个6自由度运动学结构具有闭合形式的运动学逆解：
????????1、三个连续的转动关节的轴相交于同一点
????????2、三个连续的转动关节的轴平行
????????为简化逆解的运算，现今的机械臂厂家生产的机械臂大多满足这一准则，几乎都有三根相交轴，如常见的PUMA560：
?????????PUMA560是一款具有球形腕的机械臂，其关节4、5、6的旋转轴相交于第五个关节坐标系的原点处，我们在逆运动学求解的过程中，通常也会选择该点作为求解的切入点：该点的位置可以表示为给定末端执行器的位置和方向的函数，同时还可以表示为数量被约简的关节变量的函数。这等价于将逆运动学问题表示为两个子问题，因为位置解和方向解被解耦了。
? ? ? ? 具体求解过程可以为：
?Pieper论文的摘要：
????????The kinematics of manipulators is studied. A model is presented which allows for the systematic description of new and existing manipulators. Six degree-of-freedom manipulators are studied. Several solutions to the problem of finding the manipulator configuration leading to a specified position and orientation are presented. Numerical as well as explicit solutions are given. The problem of positioning a multilink digital arm is also discussed. Given the solution to the position problem, a set of heuristics is developed for moving a six degree-of-freedom manipulator from an initial position to a final position through a space containing obstacles. This results in a computer program shown to be able to direct a manipulator around obstacles.
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