Mechanics of Closed Chains

Eclipse Family of Parallel Mechanisms

Exploiting Redundant Actuation


Mechanics of Closed Chains


The papers below describe our work on the kinematic and dynamic modeling, performance analysis, optimal design, and calibration of closed chains. The unifying thread in our work is the application of tools from modern differential geometry to characterize, e.g., manipulability, kinematic singularities, and design parameter sensitivity for the most general kinematic chains containing closed loops, the presence of both passive and active joints, and possibly redundant actuation. Our latest work focuses on ways to design mechanisms with reduced vibration characteristics---in a recent paper we show how maximizing the lowest natural frequency of a mechanism with respect to the inertial parameters can be framed as a convex programming problem.



Eclipse mechanism in an actuator singularity configuration

Related Publications

F.C. Park, ``Optimal robot design and differential geometry," Trans. ASME Special 50th Anniv. Design Issue, vol. 117(B), pp. 87-92, 1995.

F.C. Park and J.W. Kim, ``Manipulability of closed kinematic chains," ASME J. Mechanical Design, vol. 120, no. 4, pp. 542-548, December 1998.

F.C. Park and J.W. Kim, ``Singularity analysis of closed kinematic chains," ASME J. Mechanical Design, vol. 121, no. 1, pp. 32-38, March 1999.

F.C. Park, J.H. Choi, and S.R. Ploen, ``Symbolic formulation of closed chain dynamics in independent coordinates," Mechanism and Machine Theory, vol. 34, no. 5, pp. 731-751, 1999.

J.W. Kim, C.B. Park, F.C. Park, J. Kim, ¡°Performance analysis of parallel mechanism architectures for CNC machining applications,¡± ASME J. Manufacturing Science and Engineering, vol. 122, no. 4, pp. 753-760, 2000.

Jinwook Kim, Jongwon Kim, and F.C. Park, ¡°Direct kinematic analysis of 3-RS parallel mechanisms," Mechanism and Machine Theory, vol. 36, no. 10, p. 1121-1134, October 2001.

Chanhee Han, Jinwook Kim, Jongwon Kim, and F.C. Park, ¡°Kinematic sensitivity analysis of the 3-UPU mechanism,¡± Mechanism and Machine Theory, vol. 37, pp. 787-798, 2002.

Yonghoon Lee, Cornel Iurascu, Youngmo Han, F.C. Park, ¡°Simulation-based actuator selection for redundantly acctuated robot mechanisms,¡± J. Robotic Systems, vol. 19, no. 8, pp. 379-390, 2002.

Cornel Iurascu and F.C. Park, "Geometric algorithms for closed chain kinematic calibration," ASME J. Mechanical Design, vol. 125, no.1, pp. 23-32, 2003.

Bokman Lim and F.C. Park, "Minimum vibration mechanism design via convex programming," ASME J. Mechanical Design, 2007 (under review).


Eclipse Family of Parallel Mechanisms


In collaboration with colleague and project leader Jongwon Kim, we have developed what we believe to be the first family of parallel mechanisms capable of 90 degree tilting angles. Several members of the Eclipse family are shown in the figures and videos below. The first prototype Eclipse I is capable of five-face machining in a single setup, and was exhibited at the 2000 EMO Machine Tool Exhibition in Paris. The Eclipse RP is a rapid prototyping system based on the Eclipse I architecture. The Eclipse II family is capable of continuous 360 degree rotations about arbitrary axes, and has been developed as a motion simulator for entertainment and flight training applications.




EMO Eclipse (photo courtesy Jongwon Kim).


  Eclipse RP (photo courtesy Jongwon Kim). Eclipse II motion simulator (photo courtesy Jongwon Kim).

Related Publications

Jongwon Kim, F.C. Park, S.J. Ryu, Jinwook Kim, Jaechul Hwang, Changbeom Park, C. Iurascu, ``Design and analysis of a redundantly actuated parallel mechanism for rapid machining," IEEE Trans. Robotics and Automation, vol. 17, no. 4, pp. 423-434, 2001.

Jongwon Kim, K.S. Cho, J.C. Hwang, C.C. Iurascu, F.C. Park, ¡°Eclipse-RP: A new RP machine based on repeated deposition and machining,¡± Pro. Inst. Mechanical Engineers K--J. Multibody Dynamics, vol. 26, no. 1, pp. 13-20, March 2002.

Jongwon Kim, Jaechul Hwang, Jinsung Kim, C.C. Iurascu, F.C. Park, Youngman Cho, "Eclipse-II: A New Parallel Mechanism Enabling Continuous 360-degree Spinning Plus Three-axis Translational Motions" IEEE Transactions on Robotics and Automation, 18(3), pp. 367 -373 June 2002.

Jongwon Kim, Young Man Cho, F.C. Park, and Jang Moo Lee, ``Design of a parallel mechanism platform for simulating six degrees of freedom general motion including continuous 360-degree spin," CIRP Annals, vol. 52, no. 1, pp. 347-350, 2003.



Exploiting Redundant Actuation


We are currently investigating ways to exploit redundant actuation to enhance the performance of parallel mechanisms. As is well-known, one of the disappointments of parallel mechanism architectures is that they did not deliver the superior stiffness characteristics that people had been expecting; the flurry of activity, and release of commercial prototypes, of parallel mechanism-based machine tools that we witnessed in the latter half of the 90s has now given way to a quiet recognition that much work remains before parallel mechanism machine tools can be made into a commercially viable technology.

We are investigating actuation strategies for enhancing the end-effector stiffness of parallel mechanisms, in the hopes that redundant actuation can increase machine stiffness, in addition to overcoming singularities and mitigating the effects of joint backlash and tolerances. We are also developing a new hybrid force-position-stiffness control paradigm for redundantly actuated closed chains.



Hybrid force-position-stiffness control paradigm for redundantly actuated closed chains.