International Journal of Mechanical Engineering Education 33/3 Instantaneous center of rotation and singularities of planar parallel manipulators H. R. Mohammadi Daniali Department of Mechanical Engineering, Faculty of Engineering, Mazandaran University, Babol, Mazandaran, Iran E-mail: mohammadi@nit.ac.ir Abstract With regard to planar parallel manipulators, a general classification of singularities into three groups is given. The classification scheme relies on the properties of instantaneous centers of rotation. This method is very fast and can easily be applied to the manipulators under study. The method is applied to a planar three-degrees-of-freedom parallel manipulator and all its singular configurations are found. Keywords planar; parallel manipulator; singularity; instantaneous center of rotation Introduction Parallel manipulators consist of multiple branches acting on a common payload platform. They have superiorities over serial ones, which include greater stiffness, improved accuracy and dynamic characteristics, higher payload/weight ratio and higher operating speeds. These advantages stem from multiple support and the fact that all the motors are fixed to the base. However, near singular configurations, all manipulators experience poor performances, and parallel manipulators are not exempt form this rule. Therefore, they lose their advantages over serial manipu- lators at these configurations. A manipulator singularity occurs at the coincidence of different direct or inverse kinematic solutions. The latter are understood here as the computation of the values of driving-joint variables from given Cartesian variables, while the former (direct kinematics) are defined as the computation of the values of the Cartesian variables from given driving-joint variables. Algebraically, singularity amounts to a rank defi- ciency of the Jacobian matrices; geometrically, singularity is observed whenever the manipulator gains some additional, uncontrollable degrees of freedom (dof), or loses some dof. Similarly, the force transmission performance of a parallel manipulator is very poor near singular configurations. The concept of singularity has been extensively studied in connection with serial manipulators [1–3]. As regards manipulators with kinematic loops, the literature is more limited [4–10]. Litvin et al. [2] used coordinate transformation matrices to locate singular configurations, while Merlet [5] proposed a method based on Grassmann line geometry. Zlatanov et al. [6, 7] classified singularities via motion–space and velocity–space models. Notash [8] found singular configurations based on the concept of screw theory. However, the classical method to locate singular configurations relies on the properties of the Jacobian matrices of the manipulator [9].