This paper presents a new geometric and recursive algorithm for analytically computing the forward dynamics of heavy-duty parallel-serial mechanisms. Our solution relies on expressing the dynamics of a class of linearly-actuated parallel mechanism to a lower dimensional dual Lie algebra to find an analytical solution for the inverse dynamics problem. Thus, by applying the articulated-body inertias method, we successfully provide analytic expressions for the total wrench in the linear-actuator reference frame, the linear acceleration of the actuator, and the total wrench exerted in the base reference frame of the closed loop. This new formulation allows to backwardly project and assemble inertia matrices and wrench bias of multiple closed-loops mechanisms. The final algorithm holds an O(n) algorithmic complexity, where $n$ is the number of degrees of freedom (DoF). We provide accuracy results to demonstrate its efficiency with 1-DoF closed-loop mechanism and 4-DoF manipulator composed by serial and parallel mechanisms. Additionally, we release a URDF multi-DoF code for this recursive algorithm.

翻译：本文提出了一种新的几何与递归算法，用于解析计算重型串并联机构的正向动力学。我们的解法依赖于将一类线性驱动并联机构的动力学降至低维对偶李代数，从而获得逆动力学问题的解析解。通过应用刚体惯性方法，我们成功给出了线性驱动器参考系中的总力螺旋、驱动器的线性加速度以及闭环节基座参考系中总力螺旋的解析表达式。这种新公式允许对多个闭环节机构的惯性矩阵和力螺旋偏置进行反向投影与组装。最终算法的复杂度为O(n)，其中$n$为自由度数量。我们提供了精度结果，以展示其在1自由度闭环节机构和由串联与并联机构组成的4自由度机械臂上的有效性。此外，我们还发布了该递归算法的URDF多自由度代码。