• Journal of Institute of Control, Robotics and Systems
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• v.13 no.4
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• pp.320-328
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• 2007

This paper presents a stiffness modeling of a low-DOF parallel robot, which takes into account of elastic deformations of joints and links, A low-DOF parallel robot is defined as a spatial parallel robot which has less than six degrees of freedom. Differently from serial chains in a full 6-DOF parallel robot, some of those in a low-DOF parallel robot may be subject to constraint forces as well as actuation forces. The reaction forces due to actuations and constraints in each serial chain can be determined by making use of the theory of reciprocal screws. It is shown that the stiffness of an F-DOF parallel robot can be modeled such that the moving platform is supported by 6 springs related to the reciprocal screws of actuations (F) and constraints (6-F). A general $6{\times}6$ stiffness matrix is derived, which is the sum of the stiffness matrices of actuations and constraints, The compliance of each spring can be precisely determined by modeling the compliance of joints and links in a serial chain as follows; a link is modeled as an Euler beam and the compliance matrix of rotational or prismatic joint is modeled as a $6{\times}6$ diagonal matrix, where one diagonal element about the rotation axis or along the sliding direction is infinite. By summing joint and link compliance matrices with respect to a reference frame and applying unit reciprocal screw to the resulting compliance matrix of a serial chain, the compliance of a spring is determined by the resulting infinitesimal displacement. In order to illustrate this methodology, the stiffness of a Tricept parallel robot has been analyzed. Finally, a numerical example of the optimal design to maximize stiffness in a specified box-shape workspace is presented.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.27 no.1
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• pp.18-25
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• 2003

A haptic hand controller (HHC) operated by the user’s hand can receive information on position and orientation of the hand and display force and moment generated in the virtual environment to the hand. In this paper, a 3-DOF hand controller is first presented, in which all the actuators are mounted on the fixed base by combining a 5-bar linkage and a gimbal mechanism. The 6-DOF HHC is then designed by connecting these two 3-DOF devices through a handle which consists of a screw and nut. Analysis using performance index is carried out to determine the dimensions of the device. The HHC control system consists of the high-level controller for kinematic and static analysis and the low-level controller for position sensing and motor control. The HHC used as a user interface to control the mobile robot in the virtual environment is given as a simple application.