• 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.

• Proceedings of the KSME Conference
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• 2004.11a
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• pp.573-578
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• 2004

This paper presents a methodology for the stiffness analysis of a low-DOF parallel manipulator. A low-DOF parallel manipulator is a spatial parallel manipulator which has less than six degrees of freedom. The reciprocal screws of actuations and constraints in each leg can be determined by making use of the theory of reciprocal screws, which provide information about reaction forces due to actuations and constraints. When pure force is applied to a leg, the leg stiffness is modeled as a linear spring along the line. For pure couple, it is modeled as a rotational spring about the axis. It is shown that the stiffness model of an F-DOF parallel manipulator consists of F springs related to actuations and 6-F springs related to constraints connected from the moving platform to the base in parallel. The $6{\times}6$ Cartesian stiffness matrix is obtained, which is the sum of the Cartesian stiffness matrices of actuations and constraints. Finally, a 3-UPU parallel manipulator is used as an example to demonstrate the methodology.

• Journal of the Korean Society for Precision Engineering
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• v.26 no.8
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• pp.79-88
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• 2009

This paper presents the analytical stiffness analysis method for a low-DOF planar parallel manipulator. An n-DOF (n<3) planar parallel manipulator to which 1- or 2-DOF serial mechanism is connected in series may be used as a positioning device in planar tasks requring high payload and high speed. Differently from a 3-DOF planar parallel manipulator, an n-DOF planar parallel counterpart may be subject to constraint forces as well as actuation forces. Using the theory of reciprocal screws, the planar stiffness is modeled such that the moving platform is supported by three springs related to the reciprocal screws of actuations (n) and constraints (3-n). Then, the spring constants can be precisely determined by modeling the compliances of joints and links in serial chains. Finally, the stiffness of two kinds of 2-DOF planar parallel manipulators with simple and complex springs is analyzed. In order to show the effectiveness of the suggested method, the results of analytical stiffness analysis are compared to those of numerical stiffness analysis by using ADAMS.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.29 no.5 s.236
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• pp.680-688
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• 2005

This paper presents a methodology for the stiffness analysis of a low-DOF parallel manipulator. A low-DOF parallel manipulator is a spatial parallel manipulator which has less than six degrees of freedom. The reciprocal screws of actuations and constraints in each leg can be determined by making use of the theory of reciprocal screws, which provide information about reaction forces due to actuations and constraints. When pure farce is applied to a leg, the leg stiffness is modeled as a linear spring along the line. For pure couple, it is modeled as a rotational spring about the axis. It is shown that the stiffness model of an it_DOF parallel nipulator consists of F springs related to actuations and 6-F springs related to constraints connected from the moving platform to the base in parallel. The 6x f Cartesian stiffness matrix is derived, which is the sum of the Cartesian stiffness matrices of actuations and constraints. Finally, the 3-UPU, 3-PRRR, and Tricept parallel manipulators are used as examples to demonstrate the methodology.

• Journal of the Korean Society of Manufacturing Technology Engineers
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• v.23 no.2
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• pp.164-172
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• 2014

This paper presents a method for analyzing the stiffness of full and low DOF (degree of freedom) planar parallel manipulators with serially connected legs. The individual stiffness of each leg is obtained by applying reciprocal screws to the leg twist using passive joints and elastic elements consisting of actuators and links. Because the legs are connected in parallel, the manipulator stiffness is determined by summing the individual leg stiffness values. This method does not require the assumption that springs should be located along reciprocal screws and is applicable to a planar parallel manipulator with a generic or singular configuration. The stiffness values of three planar parallel manipulators with different DOFs are analyzed. The numerical results are confirmed using ADAMS S/W.