Forward problem singularities in parallel manipulators which generate SX–YS–ZS structures Raffaele Di Gregorio * Department of Engineering, University of Ferrara, Via Saragat, 1; 44100 Ferrara, Italy Received 26 May 2004; received in revised form 11 October 2004; accepted 15 October 2004 Available online 8 December 2004 Abstract The instantaneous forward problem (IFP) singularities of a parallel manipulator (PM) must be deter- mined during the manipulator design and avoided during the manipulator operation, because they are con- figurations where the end-effector pose (position and orientation) cannot be controlled by acting on the actuators any longer, and the internal loads of some links become infinite. When the actuators are locked, PMs become structures consisting of one rigid body (platform) connected to another rigid body (base) by means of a number of kinematic chains (legs). The geometries (singular geometries) of these structures where the platform can perform infinitesimal motion correspond to the IFP singularities of the PMs the structures derive from. In this paper, the singular geometries of the structures with topology SX–YS–ZS (S stands for spherical pair, whereas X, Y and Z stand for three generic one-dof pair which may be or may not be of the same type) are studied with a unified approach. The presented approach leads to obtain an analytic condition which allows all the singular geometries of these structures to be determined. More- over, the geometric interpretation of the found singularity condition and the exhaustive enumeration of the types of singular geometries is provided. Finally, the use of the presented results in the design of the manip- ulators which become one structure with topology SX–YS–ZS when the actuators are locked is discussed. Ó 2004 Elsevier Ltd. All rights reserved. Keywords: Kinematics; Parallel mechanisms; Mobility analysis; Singularities 0094-114X/$ - see front matter Ó 2004 Elsevier Ltd. All rights reserved. doi:10.1016/j.mechmachtheory.2004.10.004 * Tel.: +39 0532 974828; fax: +39 0532 974870. E-mail address: rdigregorio@ing.unife.it www.elsevier.com/locate/mechmt Mechanism and Machine Theory 40 (2005) 600–612 Mechanism and Machine Theory