Kinetostatics and Dynamics of Redundantly Actuated Planar Parallel Link Mechanisms

Abstract

Robotic systems with parallel link mechanisms (PLMs) have mechanical characteristics such as rigidity of the mechanism and precise positioning (Stewart, 1966), (Merlet 2006), (Wang & Liu, 2008). These characteristics enable them to stably perform contact tasks with sensitive force, e.g. mold grindings and rehabilitation robotics. On the other hand, mechanical interference and the singularity of the mechanisms (Merlet, 1989) restrict the robot’s movable range. PLMs have therefore been conventionally applied not to general-purpose industrial robots, but to special-purpose machines (Weck, 2002), (Oiwa, 1997). In order to expand this limited application of PLMs, we have proposed a new parallel link mechanism with multi drive linear motors (MDLMs) (Harada & Nagase, 2009, 2010). The multi drive is a control method for linear motors in which a number of moving parts are individually driven on one stator part. We have proposed various configurations of PLMs which have been constructed for MDLMs. These PLMs expand the robot’s movable range while retaining the advantageous rigid mechanism and precise positioning that PLMs offer. Moreover, the proposed PLMs are suitable for force control, because the linear motors are directory driven without friction full gearings. Several studies related to expanding the movable range of the PLM have previously been published (Honegger et al., 1997), (Kim et al., 2003), (Liu et al., 2004), (In et al., 2008), (Milutinovis et al., 2005), (Zhang, 2008). Notably, redundantly actuated 3-DOF xy planar PLMs on linear actuators (Zhang, 2008), (Wang et al., 2008), (Marquet et al., 2001) have been proposed as mechanisms that are similar to our PLM. A two 2-DOF PRRRP (P denotes prismatic joint and R denotes rotational) parallel manipulator (Liu et al., 2007) has been employed as a mechanical element of these planar PLMs, including ours. However, these planar PLMs, excluding ours, aim at position control, not at force control. Conventionally, gearings or ball screws are used for the actuator transmission of PLMs. However, it is difficult to compensate for the undesired internal force among the redundant link mechanisms with the position controlled actuators. This undesired internal force results in mechanical deformation around the transmission parts (Leong et al., 2004). Our PLM is suitable for force control, because it employs directly driven linear motors. It can control the internal force and compensate for the mechanical deformation because of the favorable effect of force control and the back-drivability of the directly driven linear motors.