• 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.

• Advances in robotics research
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• v.1 no.2
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• pp.141-154
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• 2014

Redundant parallel manipulators have some advantages over the nonredundant parallel manipulators. It is important to determine how many additional branches should be introduced. This paper studies whether one or two additional branches should be added to a 3-DOF parallel manipulator by comparing the flexible deformation of a 3-DOF parallel manipulator with one additional branch and that with two additional branches. The kinematic and dynamic models of the redundant parallel manipulator are derived and the flexible deformation is investigated. The flexible deformation of the manipulators with one additional branch and two branches is simulated and compared. This paper is helpful for designers to design a redundantly actuated parallel manipulator.

• 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 of Manufacturing Technology Engineers
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• v.20 no.3
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• pp.322-328
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• 2011

This paper presents inverse kinematics and workspace analysis of a planar three degree-of-freedom (DOF) parallel manipulator. Furthermore, optimization problem of the manipulator is presented. The manipulator adopts PRR (Prismatic-Revolute-Revolute) mechanism and the prismatic actuators are fixed to the base. This leads to a reduction of the inertia of the moving links and hence enables it to move with high speed. The actuators are linear electric motors. First, the mechanism based on the geometry of the manipulator is introduced. Second, a workspace analysis is performed. Finally, design optimization is carried out to have large workspace. The proposed approach can be applied to the design optimization of various three DOF parallel manipulators in order to maximize their workspace. The performance of mechanism is improved and satisfies the requirements of workspace to align micro-components.

• 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 Institute of Control, Robotics and Systems
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• v.5 no.3
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• pp.324-337
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• 1999

In this work, a new 3-PSP type spatial 3-degree-of-freedom parallel mechanism is proposed. And a 6 DOF hybrid manipulator which consists of a 3-PPR type planar 3 DOF parallel mechanism and a new 3-PSP type spatial 3-degree-of-freedom parallel mechanism is proposed. Both 3 DOF mechanism modules have closed-form forward position solutions and particularly, 3-PSP spatial module has unique forward position solution. Firstly, the closed-form position analysis and first-order kinematic analysis for the proposed 3-PSP type module are carried out, and the first-order kinematic characteristics are examined via maximum singular value and the isotropic index of the mechanism. It is shown through these analyses that the mechanism has excellent isotrpic property throughout the workspace. Secondly, position and kinematic analysis of the 3-PPR planar module are briefly described. Thirdly, the forward position analysis for the 3-PPR 3-PSP type 6 degree-of-freedom hybrid mechanism consisting of a 3-PPR planar module and a 3-PSP spatial module is performed along with the analysis of the workspace size and first-order kinematic characteristics. The kinematic characteristics of the proposed hybrid manipulator are compared to those of geometrically similar Stewart manipulator.

• Transactions of the Korean Society of Machine Tool Engineers
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• v.13 no.3
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• pp.44-52
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• 2004

This paper proposed a error compensation methodology for three-DOF translational parallel manipulator. The proposed method uses CMM (coordinate measuring machine) as metrology equipment to measure the position of end-effector. To identify the transform relationships between the coordinate system of the parallel manipulator and the CMM coordinate system, a new coordinate referencing (or coordinate system identification) technique is presented. By using this technique, accurate coordinate transformation relationships are efficiently established. According to these coordinate transformation relationships, an equation to calculate the compensating error components at any arbitrary position of the end-effector is derived. In this paper, Monte Carlo simulation method is applied to simulate the compensation process. Through the simulation results, the proposed error compensation method proves its effectiveness and feasibility.

• Proceedings of the Korean Society of Precision Engineering Conference
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• 2006.10a
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• pp.539-540
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• 2006

• Journal of the Korean Society of Industry Convergence
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• v.17 no.3
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• pp.84-92
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• 2014

In this paper, a novel 5-axis hybrid-kinematic machine tool is introduced and the research results on accuracy improvement of the prototype machine tool are presented. The 5-axis hybrid machine tool is made up of a 3-DOF parallel manipulator and a 2-DOF serial one connected in series. The machine tool maintains high ratio of stiffness to mass due to the parallel structure and high orientation capability due to the serial-type wrist. In order to acquire high accuracy, the methodology of measuring the output shafts by additional sensors instead of using encoder outputs at the motor shafts is proposed. In the kinematic view point, the hybrid manipulator reduces to a serial one, if the passive joints in the U-P serial chain at the center of the parallel manipulator are directly measured by additional sensors. Using the method of successive screw displacements, the kinematic error model is derived. Since a ball-bar is less expensive than a full position measurement device and sufficiently accurate for calibration, the kinematic calibration method of using a ball-bar is presented. The effectiveness of the calibration method has been verified through the simulations. Finally, the calibration experiment shows that the position accuracy of the prototype machine tool has been improved from 153 to $86{\mu}m$.

• Journal of the Korean Society for Precision Engineering
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• v.15 no.1
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• pp.60-68
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• 1998

Parallel link manipulators have an ability of more precise positioning than serial open-loop manipulators. However. general parallel link manipulators have been restricted to the real applications since they have limited workspace due to interference among actuators. In this study, we suggest a closed-loop manipulator with 6 degrees-of-freedom and with enlarged workspace. It consists of two parts for minimizing the interference among actuators. One part is lower structure with planar 3 degrees-of-freedom and the other is upper one with spatial 3 degrees-of-freedom. Forward kinematics and inverse kinematics are solved, research about singularity points are carried out and workspace is evaluated. The comparison of workspace between Stewart platform, which is the typical parallel link manipulator, and the suggested manipulator shows that the workspace of the latter is wider than that of the former. Especially, simulation results also show that the suggested manipulator is more suitable when there needs rotation in the end-effector.