Operation mode analysis of 3-RPS parallel manipulators based on their design parameters

It is known that a 3-RPS parallel manipulator with an equilateral triangle base and an equilateral triangle platform has two operation modes (Schadlbauer et al., 2014) whereas a 3-RPS cube manipulator with a cube shaped base and an equilateral triangle platform has only one operation mode (Nurahmi et al., 2014). This behavior is indeed a result of the difference in the architectures of these manipulators. Therefore, this paper deals with the operation mode analysis of 3-RPS parallel manipulators based on their design parameters. Study's kinematic mapping is exploited to derive the constraint equations of the manipulators under study. A linear combination of the constraint equations independent of the joint variables is compared with a general quadric in the 7-dimensional projective space P7 to obtain some relations between the design parameters of 3-RPS manipulators with coplanar revolute joints, such that those manipulators have two operation modes. Some special cases and a numerical example are considered to emphasize the proposed approach and highlight the contributions of the paper.