Parallel kinematic manipulators (PKM) are characterized by closed kinematic loops, due to the parallel arrangement of limbs but also due to the existence of kinematic loops within the limbs. Moreover, many PKM are built with limbs constructed by serially combining kinematic loops. Such limbs are called hybrid, which form a particular class of complex limbs. Design and model-based control requires accurate dynamic PKM models desirably without model simplifications. Dynamics modeling then necessitates kinematic relations of all members of the PKM, in contrast to the standard kinematics modeling of PKM, where only the forward and inverse kinematics solution for the manipulator (relating input and output motions) are computed. This becomes more involved for PKM with hybrid limbs. In this paper a modular modeling approach is employed, where limbs are treated separately, and the individual dynamic equations of motions (EOM) are subsequently assembled to the overall model. Key to the kinematic modeling is the constraint resolution for the individual loops within the limbs. This local constraint resolution is a special case of the general \emph{constraint embedding} technique. The proposed method finally allows for a systematic modeling of general PKM. The method is demonstrated for the IRSBot-2, where each limb comprises two independent loops.

翻译：并联运动学机械臂（PKM）的特征在于其封闭运动学回路，这既源于支链的并行排列，也由于支链内部运动学回路的存在。此外，许多PKM的支链通过串联组合运动学回路构建而成。此类支链被称为混合支链，构成了一类特殊的复杂支链。基于模型的设计与控制需要精确的PKM动力学模型，且最好无需进行模型简化。动力学建模因此需要PKM所有构件的运动学关系，这与PKM的标准运动学建模形成对比——后者仅计算机械臂的正向与逆向运动学解（关联输入与输出运动）。对于具有混合支链的PKM，这一过程变得更为复杂。本文采用模块化建模方法，将支链分别处理，随后将各支链的运动方程（EOM）组装为整体模型。运动学建模的关键在于支链内部各独立回路的约束解析。这种局部约束解析是通用\emph{约束嵌入}技术的特例。所提出的方法最终实现了对通用PKM的系统化建模。本文以IRSBot-2为例演示了该方法，其中每个支链包含两个独立回路。