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Direct kinematics of a double parallel robot arm for real time velocity control


The determination of the direct kinematics of a parallel mechanism is a difficult problem but must be solved for practical application. This paper presents the efficient formulation of the direct kinematics and the Jacobian of a double parallel robot arm for velocity control. The robot arm consists of two parallel mechanisms, and a central axis that generates positional and orientational motions independently. Given a set of lengths for the linear actuators, the direct kinematics computes the position and orientation of the end-effector, and the Jacobian transforms the velocities of the end-effector to those of the linear actuators. The developed formulation is implemented in a real-time control setting and its efficiency is demonstrated.

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  1. Baron, L. and Angeles, J., 1994, “The Decoupling of the Direct Kinematics of Parallel Manipulators Using Redundant Sensors.”Proc IEEE Int. Conf. Robotics and Automation. SanDiego, pp. 974–979.

  2. Cheok, K. C., Overholt, J. L. and Beck, R. R. 1993, “Exact Methods for Determining the Kinematics of a Stewart Platform Using Additional Displacement Sensors,”J. Rob. Syst. 10 (5), pp. 689–707.

  3. Gosselin, C. 1990. “Determination of the Workspace of 6-Dof Parallel Manipulators.”J. of Mechanism and Design, pp. 331–336.

  4. Gosselin, C. and Angeles, J., 1990, “Singularity Analysis of Closed-Loop Kinematic Chains,”IEEE Trans. Robotics and Automation, Vol. 6, No. 3, pp. 281–290.

  5. Lee, M. K., 1995. “Design of a High Stiffness Machining Robot Arm with Double Parallel Mechanism,”J. of KSME in Korea, Vol. 19 No. 1, pp. 22–37.

  6. Lee, M. K., 1995. “Dynamic Analysis of a Double Parallel Robot Arm,”J. of KSME in Korea, Vol. 19 No. 11, pp. 2912–2926.

  7. Merlet, J. P., 1993. “Direct Kinematics of Parallel Manipulators,”IEEE Trans. on Robotics and Automation, Vol. 9, No. 6, pp. 842–846.

  8. Mohamed, M. G. and Duffy, J. 1985. “A Direct Determination of the Instantaneous Kinematics of Fully Parallel Robot Manipulators,”ASME J. of Mechanisms, Transmissions, and Automation in Design, Vol. 107, pp. 226–229.

  9. Raghavan, M., 1991, “The Stewart Platform of General Geometry has 40 Configurations,”ASME Press in Advances in Design Automation. pp. 397–402.

  10. Sugimoto, K., 1987. “Kinematic and Dynamic Analysis of Parallel Manipulators by Means of Motor Algebra,”ASME J. of Mechanisms, Transmission, and Automation in Design, Vol. 109, pp. 3–7.

  11. Zanganeh, K. E. and Angeles, J., 1995, “Real-Time Direct Kinematics of General Six-Degree of Freedom Parallel Manipulators with Minimum Sensor Data,”J. of Robotic Systems, Vol. 12, No. 12, pp. 833–844.

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Correspondence to Kun Woo Park.

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Department of Control and Instrumentation Engr.

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Lee, M.K., Park, K.W. Direct kinematics of a double parallel robot arm for real time velocity control. KSME International Journal 12, 525–535 (1998).

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Key Words

  • Double Parallel Mechanism
  • Direct Kinematics
  • Geometric Constraint
  • Link Train
  • Active and Passive Joints
  • Jacobian
  • Computational Time
  • Velocity Control
  • Workspace