• 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 Institute of Control, Robotics and Systems
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• v.6 no.2
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• pp.181-189
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• 2000

This paper presents the optimal redundant actuation of parallel manipulators for complicated robotic applications such as cutting grinding drilling and digging that require a high degree of operational stiffness as well as the balance between force applicability and dexterity. First by taking into account the distribution(number and location) of active joints the statics and the operational stiffness of a redundant parallel manipulator are formulated and the effects of actuation redundancy are analyzed, Second for given task requirements including joint torque limit task force maximum allowable disturbance and maximum allowable deflection the task execution conditions of a redundant parallel manipulator are derived and the efficient testing formulas are provided. Third to achieve high operational stiffness while maintaining moderate dexterity the redundant actuation of a parallel manipulator is optimized which determines the optimal distribution of active joints and the optimal internal joint torque, Finally the simulation results for the optimal redundant actuation of a planar parallel manipulator are given.

• Proceedings of the Korean Society of Precision Engineering Conference
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• 1997.10a
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• pp.397-401
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• 1997

An error analysis is very important for a precision machine to estimate its performances. This study deals with error of a new parallel device, cubic parallel manipulator. There are so many error sources in this mechanism. Errors of the cubic parallel device vary depending on the stiffness of the manipulator. The stiffness of each link depends on the directions of the link and actuation force. In this paper, the stiffness of the manipulator is calculated by ARAQUS and the position and orlentation errors are predicted within a given workspace. The analysis shows that the method can be used in predicting the accuracy of other parallel devices and in designing parallel devices.

• Journal of Mechanical Science and Technology
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• v.17 no.4
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• pp.528-537
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• 2003

This paper proposes a 3-PPR planar parallel manipulator, which consists of three active prismatic Joints, three passive prismatic joints, and three passive rotational joints. The analysis of the kinematics and the optimal design of the manipulator are also discussed. The proposed manipulator has the advantages of the closed type of direct kinematics and a void-free workspace with a convex type of borderline. For the kinematic analysis of the proposed manipulator, the direct kinematics, the inverse kinematics, and the inverse Jacobian of the manipulator are derived. After the rotational limits and the workspaces of the manipulator are investigated, the workspace of the manipulator is simulated. In addition, for the optimal design of the manipulator, the performance indices of the manipulator are investigated, and then an optimal design procedure Is carried out using Min-Max theory. Finally. one example using the optimal design is presented.

• Proceedings of the Korean Society of Precision Engineering Conference
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• 2000.11a
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• pp.207-210
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• 2000

Singular points are those at which the determinant of a Jacobian matrix is zero. A parallel manipulator gains mostly an extra DOF at the singular points, where it can not be properly controlled. In this study, singular points of a cubic parallel manipulator are illustrated by obtaining the determinant of a Jacobian matrix mathematically, and the singular points of the manipulator are found to be three separate planes in a 3D space. The dependency among links for each singular point is determined by applying linear algebra. Also, the singular points and workspace of the cubic parallel manipulator are plotted to check if the workspace contain singular points.

• Journal of the Korean Society for Precision Engineering
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• v.20 no.3
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• pp.97-104
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• 2003

This paper proposes a new parallel manipulator fur plane motion, and then discusses on the workspace and kinematical characteristics of the manipulator. The conventional planar parallel manipulators have some disadvantages which are complex non-closed type direct kinematics, workspaces containing useless voids, and concave type border tines of workspaces. The proposed planar parallel manipulator overcomes the above disadvantages, that is, the manipulator has simple closed type direct kinematics, a void-free workspace, and a convex type borderline of a workspace. This paper shows the simulation result of the workspace as well as performances indices using a homogeneous inverse Jacobian.

• 제어로봇시스템학회:학술대회논문집
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• 2000.10a
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• pp.422-422
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• 2000

Parallel manipulators have been used to a variety of applications, including the motion simulators and mechanism for precise machining. A Stewart-Gough type parallel manipulator is composed of six linear joints which have wider contact areas than revolute ones, so linear joints are more affected by frictional force. First, the reference trajectories are computed from the model of the parallel manipulator assuming that it is subject to only the gravitational force and no friction exists. In the actual operation where friction exists, the control inputs, which correspond to the friction forces, are obtained by forcing the actual joint variables to follow these trojectories by proper control. It is shown that control performance can be improved when the friction compensation based on this information is added to the controller for position control of the moving plate of a parallel manipulator.

• Journal of the Korean Society for Precision Engineering
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• v.20 no.4
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• pp.59-67
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• 2003

This paper presents a new approach for the use of smart materials, piezoelectric materials of PVDF and PZT, for vibration attenuation of a planar parallel manipulator. Since lightweight linkages of parallel manipulators deform under high acceleration/deceleration, an active damper is needed to attenuate vibration due to structural flexibility of linkages. Based on the dynamic model of a planar parallel manipulator, an active damping controller is developed, which consists of a PD feedback control scheme, applied to linear electrical motors, and a linear velocity feedback (L-type) scheme applied to either PVDF layer or PZT actuator(5). Simulation results show that piezoelectric materials yield good damping performance, resulting in precise manipulations of a planar parallel manipulator.

• 제어로봇시스템학회:학술대회논문집
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• 1996.10b
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• pp.213-216
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• 1996

This paper studies a class of in-parallel manipulators with special geometry where the forward displacement analysis problem can be solved easier than the fully parallel manipulators. Three horizontal links of this mechanism provide 3DOFs(Degrees of Freedom), which are one degree of orientational freedom and two degrees of translatory freedom. Three vertical links of this mechanism provide 3DOFs, which are two degrees of orientational freedom and one degree of translatory freedom. The main advantages of this manipulator, compared with the Stewart platform type, are the capability to produce pure rotation and to predict the motion of the moving platform easily. Since this manipulator has simple kinematic characteristics compared with the Stewart platform, controlling in real-time is possible due to less computational burden. The purpose of this investigation is to develope an analytical method and systematic method to analyze the basic kinematics of the manipulator. The basic kinematic equations of the manipulator are derived and simulation is carried out to show the performance of the mechanism.

• 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.