Kinematics and dynamics of planar mechanisms reinterpreted in rigid-body's configuration space

详细信息    查看全文

• 作者：Raffaele Di Gregorio
• 关键词：Displacement group ; Planar displacements ; Planar mechanisms ; Configuration space
• 刊名：Meccanica
• 出版年：2016
• 出版时间：April 2016
• 年：2016
• 卷：51
• 期：4
• 页码：993-1005
• 全文大小：741 KB
• 参考文献：1.Paul B (1979) Kinematics and dynamics of planar machinery. Prentice-Hall, Englewood Cliffs
  2.Mason M (2001) Mechanics of robotic manipulation. MIT Press, Cambridge
  3.Lounesto P (2004) Introduction to Clifford algebras. In: Ablamowicz R et al (eds) Lectures on Clifford (geometric) algebras and applications. Springer, New York, pp 1–30CrossRef
  4.Hervé JM (1994) The mathematical group structure of the set of displacements. Mech Mach Theory 29(1):73–81CrossRef
  5.Bonev IA, Zlatanov D, Gosselin CM (2003) Singularity analysis of 3-dof planar parallel mechanisms via screw theory. ASME J Mech Des 125(3):573–581CrossRef
  6.Reuleaux F (1876) The kinematics of machinery. MacMillan, London
  7.Lin Q, Burdick J (2000) Objective and frame-invariant kinematic metric functions for rigid bodies. Int J Robot Res 19(6):612–625CrossRef
  8.Di Gregorio R (2008) A novel point of view to define the distance between two rigid-body poses. In: Lenarcic J, Wenger P (eds) Advances in robot kinematics: analysis and design, ARK2008. Springer, Amsterdam, pp 361–369. ISBN: 978-1-4020-8599-4
  9.Di Gregorio R (2009) Review and comparison of the metrics proposed for measuring the distance between two rigid-body poses. In: Meneghetti U, Maggiore A, Parenti-Castelli V (eds) Seconda Giornata di Studio Ettore Funaioli: 18 luglio 2008. Quaderni del DIEM, Bologna, pp 221–233. ISBN: 978-88-86909-53-2. doi:10.​6092/​unibo/​amsacta/​2552
  10.Tenenbaum RA (2004) Fundamentals of applied dynamics. Springer, New York
  11.Di Gregorio R (2009) A novel method for the singularity analysis of planar mechanisms with more than one degree of freedom. Mech Mach Theory 44(1):83–102CrossRef MATH
  12.Newton I (1687) Philosophiæ Naturalis Principia Mathematica. S. Pepys, Reg. Soc. Præses, London
  13.Pennock GR, Israr A (2009) Kinematic analysis and synthesis of an adjustable six-bar linkare. Mech Mach Theory 44(2):306–323CrossRef MATH
  14.Hunt KH (1983) Structural kinematics of in-parallel-actuated robot-arms. ASME J Mech Transm Autom Des 105(4):705–712CrossRef
  15.Gosselin CM, Sefrioui J (1991) Polynomial solutions for the direct kinematic problem of planar three-degree-of-freedom parallel manipulator. In: Proceedings of the 1991 international conference on advanced robotics, Pisa, Italy, pp 1121–1129
  16.Tsai L-W (1999) Robot analysis: the mechanics of serial and parallel manipulators. Wiley, New York
  17.Primrose EJF, Freudenstein F, Roth B (1967) Six-bar motion. Arch Ration Mech Anal 24(1):22–77MathSciNet MATH
  18.Watanabe K, Funabashi H (1984) Kinematic analysis of Stephenson six-link mechanisms. Bull Jpn Soc Mech Eng 27(234):2863–2878CrossRef
  19.Watanabe K, Katoh H (2004) Identification of motion domains of planar six-link mechanisms of the Stephenson-type. Mech Mach Theory 39(10):1081–1099CrossRef MATH
  20.Simionescu PA, Smith MR (2001) Four- and six-bar function cognates and overconstrained mechanisms. Mech Mach Theory 36(8):913–924CrossRef MATH
  21.Di Gregorio R (2008) An Algorithm for analytically calculating the positions of the secondary instant centers of indeterminate linkages. ASME J Mech Des 130(4):042303-1–042303-9CrossRef
  
• 作者单位：Raffaele Di Gregorio (1)
  
  1. Department of Engineering, University of Ferrara, Via Saragat n. 1, 44122, Ferrara, Italy
  
• 刊物类别：Physics and Astronomy
• 刊物主题：Physics
  Mechanics
  Civil Engineering
  Automotive and Aerospace Engineering and Traffic
  Mechanical Engineering
  
• 出版者：Springer Netherlands
• ISSN：1572-9648

文摘

Mechanisms with lower mobility can be studied by using tools that are directly deduced from those of spatial kinematics as screw theory. Nevertheless, ad-hoc tools that fully exploit the peculiarities of the displacement subgroups these mechanisms move in are usually more efficient both in showing mechanisms’ features and when used to conceive numerical algorithms. Planar displacements constitute a three-dimensional subgroup with many peculiarities that allow the use of simplified tools (e.g., complex numbers) for studying planar mechanisms. Here, the systematic use of three-dimensional vector spaces to represent link poses and velocities in planar motion and planar system of forces is investigated. The result is a novel coherent set of tools that make it possible to geometrically describe kinematics and dynamics of planar mechanisms in the three-dimensional configuration space of links’ planar poses. The effectiveness of this novel approach is shown through a case study.