Standing on the shoulders of giants: A brief note from the perspective of kinematics

Chinese Journal of Mechanical Engineering, Dec 2016

Xianwen Kong

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Standing on the shoulders of giants: A brief note from the perspective of kinematics

CHINESE JOURNAL OF MECHANICAL ENGINEERING Vol. 30 Standing on the Shoulders of Giants: A Brief Note from the Perspective of Kinematics 0 KONG Xianwen School of Engineering and Physical Sciences Heriot-Watt University Edinburgh EH14 4AS , UK - Kinematics[1‒3] has evolved with and contributed significantly to the human demands. For example, slider-crank mechanisms have been widely used in engines since the industrial revolution. Additionally, constant-velocity couplings have been developed to meet the needs of the automobile industry since the 1920’s. With the development of robots, robot kinematics has been one of the research focuses in Kinematics since the 1970’s. Several research areas in Kinematics, such as parallel mechanisms, compliant mechanisms, cable-driven parallel mechanisms, reconfigurable mechanisms, origami-inspired mechanisms, and biohybrid systems, have emerged in the past three decades. The development of Kinematics has been closely related to mathematics and machine design. Recent advances in computer algebra geometry and numerical algebra geometry[4‒5] have enabled in-depth analysis of multi-mode parallel mechanisms[5‒6] which requires solving polynomial equations with positive dimensional solution sets. Now, advances in software engineering, artificial intelligence, biomimetics, materials, sensing, actuation, control, and manufacturing technologies are expected to have significant impact on Kinematics in the future. For instance, the application of mechanical CAD software can free people from deriving complicated mathematical equations in solving certain kinematic problems[7‒8]. In the following, three cases will be presented to illustrate the importance and challenges in maintaining an awareness of the state-of-the-art in the research in Kinematics and certain topics which may involve old references in addition to the recent ones. The first case pertains to the closed-form determination of the crank position corresponding to the maximum slider velocity in a slider-crank mechanism. This is a fundamental problem in engine design. Although slider-crank mechanisms have been used for centuries[9], the above problem had not been solved until the publication of Refs. [10‒12] at the end of 19th century. In these publications, a cubic equation was derived using analytic or geometric approaches and then solved to obtain the crank position. However, these references were ignored for many years. This led to the publication of an alternative closed-form solution of the same problem in Ref. [13] in 1941. Refs. [10‒13] were also not known to the authors of Ref. [14], in which the slide-crank mechanism was taken as an example in the application of their approach to the analysis of four-bar linkages. Unware of the work of Refs. [10‒14], a numerical solution was presented in Ref. [15] in 1958 when the work of Refs. [10‒14] was pointed out in the discussion of Ref. [15] by the reviewers. Without knowing the work of Refs. [10‒13, 15] and based on the work of Ref. [14], a third closed-form solution was proposed in Ref. [16] in 2005 to replace the approximate solutions to this problem in textbooks. This was more than one hundred years after the publication of Refs. [10‒12]. Should the authors of Refs. [13‒16] have known the previous work in Refs. [10‒12], they may have saved both time and effort in finding their solutions. Possible causes of the unawareness of the Refs. [10‒12] might include: (a) It was not easy to access the information about these old references at that time; and (b) Some terminologies used in Refs. [10‒12] were different from those in Refs. [13‒16]. The second case is on the type synthesis of parallel mechanisms. In the first decade of the 21st century, several systematic approaches to the type synthesis of parallel mechanisms were proposed using different mathematical tools around the world[17‒27]. However, the work on the constant-velocity coupling connecting parallel axes by HUNT K H[28] published in 1973 was ignored by almost all the researchers on parallel mechanisms, although it was closely related to the type synthesis of translational parallel mechanisms. The ignorance of HUNT’s work might be caused by (a) It was on a different topic from parallel mechanisms; (b) HUNT himself did not mention his work[28] on the constant-velocity coupling in his paper[29] on the type synthesis of parallel mechanisms, which was based on the mobility equation; and (c) Not many people understood screw theory before 2000. Should researchers have known the work of Ref. [28] earlier, they would have saved much time in reinventing the 3-DOF translational parallel mechanisms. Fortunately, such ignorance led to the development of several systematic methods on the type synthesis using different approaches[17‒27] and invention of a large number of parallel mechanisms. In addition, the introduction of inactive joints in parallel mechanisms[21] provided a solid foundation for the type synthesis of parallel mechanisms with multiple operation modes[30]. It is also noted in 1960’s, HUNT and PHILLIPS J revived the screw theory published in 1900 by BALL R S. The last case is the successful extension of classic single-loop overconstrained mechanisms to the design of parallel mechanisms[21, 31, 32] and multi-mode mechanisms[31, 33], motion structure[34] or deployable systems[35] and thick-plate folding[36]. Without understanding single-loop overconstrained mechanisms, these advances would not have been possible. The above cases have demonstrated the significant impact of having awareness of the state-of-the-art in the relevant areas on the research in Kinematics. Although access to the literature has become more convenient than ever before, it is even more challenging to have full awareness of the state-of-the-art compared with decades ago when it was not easy to get the references one needed. This is because there are now so many emerging areas of research and technologies combined with a large number of new conference and journal publications. In addition to individual effort, collaboration within the same discipline and across different disciplines may provide a potential solution to meet this challenge. [1] ERDMAN A G . Modern kinematics: Developments in the last forty years [M]. New York : Wiley-Interscience, 1993 . [2] McCarthy J M . 21st century kinematics[M]. London: Springer, 2013 . [3] DING X , KONG X , DAI J S. Advances in reconfigurable mechanisms and robots II . Switzerland: Springer International Publishing, 2016 . [4] WALTER D R , HUSTY M L , PFURNER M. Chapter A : complete kinematic analysis of the SNU 3-UPU parallel manipulator [C]// BATES D J, BESANA G , Di ROCCO S , WAMPLER C W, eds, Interactions of Classical and Numerical Algebraic Geometry, Providence: American Mathematical Society , 2009 : 331 - 346 . [5] SOMMESE A J , WAMPLER II C W. The numerical solution of systems of polynomials arising in engineering and science [M]. World Scientific , 2005 . [6] KONG X. Reconfiguration analysis of a 3-DOF parallel mechanism using Euler parameter quaternions and algebraic geometry method[J]. Mechanism and Machine Theory , 2014 , 74 : 188 - 201 . [7] SCHMIEDELER J P , CLARK B C , KINZEL E C , et al. Kinematic synthesis for infinitesimally and multiply separated positions using geometric constraint programming [J]. ASME Journal of Mechanical Design , 2014 , 136 ( 3 ): 034503 . [8] JOHNSON A , KONG X , RITCHIE J M. Determination of the workspace of a three-degrees-of-freedom parallel manipulator using a three-dimensional computer-aided-design software package and the concept of virtual chains [J]. ASME Journal of Mechanisms and Robotics , 2016 , 8 ( 2 ): 024501 . [9] SEAWARD J. Remarks on the comparative advantages of long and short connecting rods and long, and short stroke engines [J]. Minutes of the Proceedings of the Institution of Civil Engineers , 1841 , 1 : 53 - 55 . [10] HILl M J M. The problem of the connecting rod [J]. Minutes of the Proceedings of the Institution of Civil Engineers , 1896 , 124 : 390 - 401 . [11] UNWIN W C. Determination of crank angle for greatest piston velocity [J]. Minutes of the Proceedings of the Institution of Civil Engineers , 1896 , 125 : 363 - 366 . [12] BURLS G A . Note on maximum crosshead velocity[J]. Minutes of the Proceedings of the Institution of Civil Engineers , 1898 , 131 : 338 - 346 . [13] VOGEL W F. Crank mechanism motions: New methods for their exact determination-III [J]. Production Engineering , 1941 , 12 ( 8 ): 423 - 428 . [14] FREUDENSTEIN F. On the maximum and minimum velocities and the accelerations in four-link mechanisms [J]. Transactions of ASME , 1956 , 78 : 779 - 787 . [15] CHING-U IP , PRICE L C. A simple formula for determining the position of maximum slider velocity in a slider-crank mechanism [J]. Transactions of ASME , 1958 , 80 : 415 - 418 . [16] ZHANG W J , LI Q. A closed-form solution to the crank position corresponding to the maximum velocity of the slider in a centric slider-crank mechanism[J] . Journal of Mechanical Design , 2006 , 128 ( 2 ): 654 - 656 . [17] FRISOLI A , CHECCACCI D , SALSEDO F , et al. Synthesis by screw algebra of translating in-parallel actuated mechanisms [C]// LENARCIC J, STANISIC M M, eds, Advances in Robot Kinematics, Norwell: Kluwer Academic Publishers, 2000 : 433 - 440 [18] LEE C C , HERVE J M. Translational parallel manipulators with doubly planar limbs [J]. Mechanism and Machine Theory , 2006 , 24 ( 4 ): 433 - 455 . [19] HUANG Z , LI Q , DING H. Theory of parallel mechanisms[M]. Dordrecht: Springer, 2013 . [20] FANG Y , TSAI L W. Analytical identification of limb structures for translational parallel manipulators [J]. Journal of Robotic Systems , 2004 , 21 ( 5 ): 209 - 218 . [21] KONG X , GOSSELIN C. Type synthesis of parallel mechanisms[M]. Berlin: Springer, 2007 . [22] YANG T L , LIU A X , LUO Y F , et al. Theory and application of robot mechanism topology [M]. Beijing: Science Press, 2012 . (in Chinese). [23] GOGU G . Structural synthesis of parallel robots: Part 1- methodology [M]. Dordrecht: Springer, 2009 [24] HE J , GAO F , MENG X , et al. Type synthesis for 4-DOF parallel press mechanism using GF set theory[J] . Chinese Journal of Mechanical Engineering , 2015 , 28 ( 4 ): 851 - 859 . [25] MENG J , LIU G F , LI Z X. A geometric theory for analysis and synthesis of sub-6 DoF parallel manipulators [J]. IEEE Transactions on Robotics , 2007 , 23 : 625 - 649 . [26] LIU X J , WANG J. Parallel kinematics: Type, kinematics, and optimal design[M]. Berlin: Springer, 2014 . [27] ZHAO J , FENG Z , CHU F , et al. Advanced theory of constraint and motion analysis for robot mechanisms [M]. Oxford : Elsevier, 2014 . [28] HUNT K H. Constant -velocity shaft couplings: A general theory[J] . Journal of Engineering for Industry 1973 , 95 ( 2 ): 455 - 464 . [29] HUNT K H. Structural kinematics of in-parallel-actuated robot-arms [J]. Journal of Mechanisms, Transmissions and Automation in Design , 1983 , 105 ( 4 ): 705 - 712 . [30] KONG X , JIN Y. Type synthesis of 3-DOF multi-mode translational/spherical parallel mechanisms with lockable joints [J]. Mechanism and Machine Theory , 2016 , 96 (Part 2): 323 - 333 . [31] KONG X , GOSSELIN C M. Type synthesis of three-degreeof-freedom spherical parallel manipulators [ J]. The International Journal of Robotics Research , 2004 , 23 ( 3 ): 237 - 245 . [32] KONG X. Type synthesis of 3-DOF parallel manipulators with both a planar operation mode and a spatial translational operation mode [J]. ASME Journal Mechanisms and Robotics , 2013 , 5 ( 4 ): 041015 . [33] KONG X , PFURNER M. Type synthesis and reconfiguration analysis of a class of variable-DOF single-loop mechanisms [J]. Mechanism and Machine Theory , 2015 , 85 : 116 - 128 . [34] ZHOU Y , CHEN Y. Motion structures: Deployable structural assemblies of mechanisms [M]. Oxon : Spon Press, 2012 . [35] QI X , HUANG H , MIAO Z , et al. Design and mobility analysis of large deployable mechanisms based on plane-symmetric Bricard linkage [J]. ASME Journal of Mechanical Design , 2016 , 139 ( 2 ): 022302 . [36] CHEN Y , PENG R , YOU Z. Origami of thick panels [J]. Science , 2015 , 349 ( 6246 ): 396 - 400 .

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Xianwen Kong. Standing on the shoulders of giants: A brief note from the perspective of kinematics, Chinese Journal of Mechanical Engineering, 2017, 1-2, DOI: 10.3901/CJME.2017.0101.001