運動全解耦並聯式機器人是一種具有特殊運動特性的並聯機構，其中每個驅動器皆可獨立控制機器人某個運動自由度，此特性在手術機器人領域中具有良好的應用潛力。Kuo&Dai[1]在2012年提出一部具四個自由度的運動全解耦並聯式微創手術機器人結構，並完成該機器人之運動分析。本研究即延續Kuo與Dai之研究成果，進行該新型機構的力量與剛度分析，探討機器人停留方位與驅動力之間的關係，以及機器人的受力與變形程度。研究首先推導機器人之Jacobian矩陣，然後搭配螺旋理論建立機器人之空間靜力平衡方程式，據此求解受刀具載重下之所需馬達輸入扭矩。接著，探討機構桿件受力變形下之剛度矩陣，以得知機器人在承受載重下桿件抗變形之能力。上述推導將搭配數個數值範例，以得知機器人於實際負載下所需的馬達扭矩與剛度特性。本研究成果可提供該新型機器人於機電整合設計之參考。

Kinematically fully-decoupled parallel robot is one special kind of parallel robots whose each motion degree-of-freedom (DOF) can be independently controlled by one corresponding actuator. Such a special robot has found its excellent application in minimally invasive surgery. In 2012, Kuo and Dai [1] reported a 4-DOF fully-decoupled parallel mechanism for minimally invasive surgery and completed its kinematic analysis. Based on Kuo and Dai’s result, this thesis aims to the force and stiffness analyses of this fully-decoupled parallel manipulator, i.e., identifying the required motor torques under the given payload for staying at the specified location and knowing the stiffness of the robot. First, we will drive the Jacobian matrix of the robot, through which the force equilibrium equations of the robot can be constructed by using screw theory. According to the force formulation, the actuation forces of the input joints within the robot workspace can be determined. Then, we investigate the stiffness matrix of the robot for learning the relationship between the payload force and the displacement of the locked robot. Several numerical examples are provided to study the real application of these formulations in the shown robot. The outcome of this study can be a reference for the mechatronic design of this new parallel robot.

[1] Kuo, C. H., Dai, J. S., 2012, “Kinematics of a Fully-Decoupled Remote Center-of-Motion Parallel Manipulator for Minimally Invasive Surgery,” ASME Journal of Medical Devices, 6(2), pp. 021008(1-12).
[2] Tsai, L. W., 1999, Robot Analysis- the Mechanics of Serial and Parallel Manipulators, John Wiley & Sons, New York.
[3] Wojtyra, M., 2009, “Joint Reactions in Rigid Body Mechanisms with Dependent Constraints,” Mechanism and Machine Theory, 44(12), pp. 2265-2278.
[4] Tsai, M. S., Yuan, W. H., 2010, “Inverse Dynamics Analysis for a 3-PRS Parallel Mechanism Based on a Special Decomposition of the Reaction Forces,” Mechanism and Machine Theory, 45(11), pp. 1491-1508.
[5] Zhao, Y., 2010, “Force Analysis of Lower-Mobility Parallel Mechanisms with Over-Constrained Couples,” Chinese Journal of Mechanical Engineering, 46(5), pp. 15-21.
[6] Li, Y. G. S., Y. M., Huang, T., Zhang, C., 2007, “Static Force Analysis of Lower-Mobility Parallel Manipulators,” Chinese Journal of Mechanical Engineering, 43(9), pp. 80-83.
[7] Lu, Y., Hu, B., Shi, Y., 2007, “Kinematics Analysis and Statics of A 2SPS+UPR Parallel Manipulator,” Multibody System Dynamics, 18(4), pp. 619-636.
[8] Lu, Y., 2007, “Using Virtual Work Theory and Cad Functionalities for Solving Active Force and Passive Force of Spatial Parallel Manipulators,” Mechanism and Machine Theory, 42(7), pp. 839-858.
[9] Hu, B., Lu, Y., 2010, “New Approach for Analyzing the Stiffness of 3-RPS Parallel Manipulator,” Chinese Journal of Mechanical Engineering, 46(1), pp. 24-29.
[10] Hu, B., Lu, Y., Xu, J. Y., 2009, “Stiffness and Singularity Analysis of 2SPS+2RPS Parallel Manipulator by Using Different Methods,” Proceedings of the 2nd International Conference on Intelligent Robotics and Applications, Singapore, 16-18 November, pp. 632-644.
[11] Gallardo, J., Rico, J. M., Frisoli, A., Checcacci, D., Bergamasco, M., 2003, “Dynamics of Parallel Manipulators by Means of Screw Theory,” Mechanism and Machine Theory, 38(11), pp. 1113-1131.
[12] Han, X. G., Cui, X. L., Chen, W. Y., 2009, “Analysis on the Instantaneous Stiffness of the 3-RPS Parallel Mechine,” Key Engineering Materials, 407, pp. 63-67.
[13] Huang, Z., Zhao, Y., Liu, J. F., 2010, “Kinetostatic Analysis of 4-R(CRR) Parallel Manipulator with Overconstraints Via Reciprocal Screw Theory,” Advances in Mechanical Engineering, pp. 1-11.
[14] Zhao, Y., Liu, J. F., Huang, Z., 2011, “A Force Analysis of a 3-RPS Parallel Mechanism by Using Screw Theory,” Robotica, 29(7), pp. 959-965.
[15] Liu, S., C Hen, Z., 2011, “Force Analysis of Single Ring Spatial Rsur Mechanism Based on Screw Theory,” Chinese Journal of Mechanical Engineering, 47(13), pp. 1-7.
[16] Ball, R. S., 1900, A Treatise on the Theory of Screws, University Press, Cambridge
[17] Hunt, K. H., 1978, Kinematic Geometry of Mechanisms Oxford University Press, Oxford
[18] Dimentberg, F. M., 1965, The Screw Calculus and Its Applications in Mechanics, Foreign Technology Division, Wright-Patterson Air Force Base, Ohio, USA. Technical Report No. FTD-HT-23-1632-67.
[19] Salisbury, J. K., 1980, “Active Stiffness Control of a Manipulator in Cartesian Coordinates,” Proceeding of the 19th IEEE Conference on Decision and Control, Albuquerque, New Mexico, OSA, 10-12 December, pp. 87-97.
[20] Gosselin, C. M., 1990, “Stiffness Mapping for Parallel Manipulator,” IEEE Transactions on Robotics and Automation, 6(3), pp. 377-382.
[21] Griffis, M., Duffy, J., 1993, “Global Stiffness Modeling of a Class of Simple Compliant Couplings,” Mechanism and Machine Theory, 28(2), pp. 207-224.
[22] Chen, S. F., Kao, I., 1998, “Simulation of Conservative Properties of Stiffness Matrices in Congruence Transformation,” Proceedings of IEEE/RSJ International Conference on Intelligent Robots and Systems, Victoria, BC, Canada, 13-17 October, pp. 311-316.
[23] Kao, I., 1999, “Properties of the Grasp Stiffness Matrix and Conservative Control Srategies,” The International Journal of Robotics Research, 18(2), pp. 159-167.
[24] Huang, C., Kao, I., 2003, “Geometrical Interpretation of the Conservative Congruence Transformation Stiffness Mapping for Serial Manipulators,” Robotics Research, Jarvis, R. A. and Eelinsky eds.,Springer Tracts in Advanced Robotics, Springer, Berlin, 6, pp. 419-431.
[25] Ei-Khasawneh, B. S., Ferreira, P. M., 1999, “Computation of Stiffness and Stiffness Bounds for Parallel Link Manipulators,” International Journal of Machine Tools & Manufacture, 39(2), pp. 321-342.
[26] Merlet, J. P., Gosselin, C. M., 2008, “Parallel Mechanisms and Robots,” Springer Handbook of Robotics, Springer-Verlag, Berlin, pp. 269-285.
[27] Quennouelle, C., Gosselin, C. M., 2008, “Stiffness Matrix of Compliant Parallel Mechanisms,” Advances in Robot Kinematics: Analysis and Design, pp. 331-341.
[28] Kuo, C. H., Dai, J. S., Dasgupta, P., 2012, “Kinematic Design Considerations for Minimally Invasive Surgical Robots: An Overview,” The International Journal of Medical Robotics and Computer Assisted Surgery, 8(2), pp. 127-145.