• 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.

• Journal of the Korean Society of Manufacturing Technology Engineers
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• v.23 no.5
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• pp.421-427
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• 2014

In this paper, the kinestatic control algorithm using a six-axis compliant device is presented. Unlike the traditional control methods using a force/torque sensor with very limited compliance, this method employs a compliant device to provide sufficient compliance between an industrial robot and a rigid environment. This kinestatic control method is used to simply control the position of an industrial robot with twists of compensation, which can be decomposed into twists of compliance and twists of freedom. A simple design method of a six-axis parallel-type compliant device with a diagonal stiffness matrix is presented. A compliant device prototype and kinestatic control hardware system and programming were developed. The effectiveness of the kinestatic control algorithm was verified through two kinds of kinestatic control experiments.

• 제어로봇시스템학회:학술대회논문집
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• 2005.06a
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• pp.631-637
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• 2005

This paper presents a stiffness analysis method for a low-DOF parallel manipulator, which takes into account of elastic deformations of joints and links. A low-DOF parallel manipulator is defined as a spatial parallel manipulator which has less than six degrees of freedom. Differently from the case of a 6-DOF parallel manipulator, the serial chains in a low-DOF parallel manipulator are subject to constraint forces as well as actuation forces. The reaction forces due to actuations and constraints in each limb can be determined by making use of the theory of reciprocal screws. It is shown that the stiffness model of an F-DOF parallel manipulator consists of F springs related to the reciprocal screws of actuations and 6-F springs related to the reciprocal screws of constraints, which connect the moving platform to the fixed base in parallel. The $6{times}6$ stiffness matrix is derived, which is the sum of the stiffness matrices of actuations and constraints. The six spring constants can be precisely determined by modeling the compliance of joints and links in a serial chain as follows; the link can be considered as an Euler beam and the stiffness matrix of rotational or prismatic joint can be modeled as a $6{times}6$ diagonal matrix, where one diagonal element about the rotation axis or along the sliding direction is zero. By summing the elastic deformations in joints and links, the compliance matrix of a serial chain is obtained. Finally, applying the reciprocal screws to the compliance matrix of a serial chain, the compliance values of springs can be determined. As an example of explaining the procedure, the stiffness of the Tricept parallel manipulator has been analyzed.

• Journal of the Society of Naval Architects of Korea
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• v.30 no.3
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• pp.116-126
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• 1993

The finite element method(FEM) has been commonly used for structural dynamic analysis. However, the direct global application of FEM to large complex structures such as ships and offshore structures requires considerable computational efforts, and remarkably more in structural dynamic optimization problems. Adoption of the component-mode synthesis method is an efficient means to overcome the above difficulty. Among three classes of the component-mode synthesis method, the free-interface mode method is recognized to have the advantages of better computational efficiency and easier implementation of substructures' experimental results, but the disadvantage of lower accuracy in analytical results. In this paper, an advanced method to improve the accuracy in the application of the free-interface mode method for the vibration analysis of large complex structures is presented. In order to compensate the truncation effect of the higher modes of substructures in the synthesis process, both residual inertia and stiffness effects are taken into account and a frequency shifting technique is introduced in the formulation of the residual compliance of substructures. The introduction of the frequency shrift ins not only excludes cumbersome manipulation of singular matrices for semi-definite substructural systems but gives more accurate results around the specified shifting frequency. Numerical examples of typical structural models including a ship-like two dimensional finite element model show that the analysis results based on the presented method are well competitive in accuracy with those obtained by the direst global FEM analysis for the frequencies which are lower than the highest one employed in the synthesis with remarkably higher computational efficiency and that the presented method is more efficient and accurate than the fixed-interface mode method.