This paper aims to study a specific kind of parallel robot: Spherical Parallel Manipulators (SPM) that are capable of unlimited rolling. A focus is made on the kinematics of such mechanisms, especially taking into account uncertainties (e.g. on conception & fabrication parameters, measures) and their propagations. Such considerations are crucial if we want to control our robot correctly without any undesirable behavior in its workspace (e.g. effects of singularities). In this paper, we will consider two different approaches to study the kinematics and the singularities of the robot of interest: symbolic and semi-numerical. By doing so, we can compute a singularity-free zone in the work- and joint spaces, considering given uncertainties on the parameters. In this zone, we can use any control law to inertially stabilize the upper platform of the robot.

翻译：本文旨在研究一类特殊的并联机器人：能够实现无限滚动的球形并联机器人（SPM）。重点关注此类机构的运动学问题，尤其考虑不确定性因素（如设计与制造参数、测量误差）及其传播效应。若要在工作空间内避免不良行为（例如奇异性影响）并实现精准控制，此类考量至关重要。本文采用符号法与半数值法两种不同途径研究目标机器人的运动学与奇异性问题。通过该方法，可在考虑参数不确定性的前提下，计算工作空间与关节空间中的无奇异区域。在该区域内，可采用任意控制律实现机器人上平台惯性稳定。