This paper proposes a method for measuring the internal and external forces of a planar 3-DOF (degree of freedom) redundantly actuated parallel mechanism. The internal forces, force acts inside the endplate and mechanism constraint force, and the external forces, forces act on the endplate and thrusts by actuators, were measured simultaneously using the axial forces of the rods. Kinetostatic equations of the parallel mechanism were used to derive algorithms for measuring the internal and external forces. A link axis force sensor was developed using a strain gauge sensor. To verify the actual internal force of the endplate, a force sensor was also installed on the endplate. A real-time system for measuring the forces of the parallel mechanism was developed using RT-Linux. The external and internal forces were measured accurately. 1. Introduction A robotic system with a parallel mechanism is mechanically characterized by high rigidity and precise positioning [1, 2]. However, the mechanical interactions and singularities of the mechanism restrict the workspace of the robot [3]. We previously proposed a 3-DOF (degree of freedom) ( ) planar parallel mechanism with four redundant actuators [4–6]. This is aimed at a table mechanism with multiaxis machine tools. By developing a characteristic mechanical design, our mechanism avoids mechanical interactions around the links. The redundant actuation of the mechanism helps avoid singular configurations that would occur with nonredundant actuation. Our mechanism expands the workspace along the horizontal direction [4] and rotational motion [6]. Several studies have considered redundantly actuated 3-DOF planar parallel mechanisms [7–9]. However, these mechanisms were aimed at position control and not force control. Force control enables complex tasks such as the grinding and polishing of mechanical parts, which require a sensitive touch. We developed a novel design for a redundantly actuated parallel mechanism by using force-controlled linear motors and installing force command–based impedance control [5]. However, friction around the linear guide or force ripples of the linear actuators may adversely affect the accuracy of the force control. Sensing the actual forces and the moment at the tip of the mechanism is an effective method for improving the accuracy and stability of the force control [10]. Certain types of linearly actuated parallel mechanisms (e.g., the Stewart platform [1] and our parallel mechanism [4]) possess the distinct advantage of straightforward mapping expression between the wrenches (forces and
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