Abstract
Mobility analysis is one of fundamental problems in kinematics and an important tool in type synthesis of linkages. In this paper, we will review screw theory as a mathematical tool for mobility analysis of overconstrained linkages and compliant mechanisms. Established by Ball in late 1800, screw theory has become one of the fundamental theories for characterizing instantaneous kinematics of spatial movements. In mid to late 1960, Waldron was one of the first modern kinematicians who systematically developed screw theory and its applications to the constraint analysis and synthesis of overconstrained linkages. Due to the screw theory, several overconstrained spatial linkages have been invented and designed, including the well known Waldron six-bar loop overconstrained linkage. In recent years, mobility analysis has been extended to compliant mechanisms which achieve motion through deflection of flexure joints. By the concept of relative compliance/ stiffness, we can also define mobility of compliant mechanisms similar to their rigid body counterparts. This paper will summarize some recent work on applying screw theory to mobility analysis and synthesis of compliant mechanisms.
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References
Waldron, K.: The constraint analysis of mechanisms. Journal of Mechanisms 1(2), 101–114 (1966)
Ball, R.S.: The Theory of Screws. Cambridge University Press, Cambridge (1998) (Originally published in 1876 and revised by the author in 1900, now reprinted with an introduction by H. Lipkin and J. Duffy)
Hunt, K.H.: Kinematic Geometry of Mechanisms. Oxford University Press, New York (1978)
Phillips, J.: Freedom in Machinery. Introducing Screw Theory, vol. 1. Cambridge University Press, Cambridge (1984)
Phillips, J.: Freedom in Machinery. Screw Theory Exemplified, vol. 2. Cambridge University Press, Cambridge (1990)
Davidson, J.K., Hunt, K.H.: Robots and Screw Theory: Applications of Kinematics and Statics to Robotics. Oxford University Press, New York (2004)
Shai, O., Pennock, G.R.: A study of the duality between planar kinematics and statics. ASME Journal of Mechanical Design 128(3), 587–598 (2006)
Waldron, K.J.: Symmetric overconstrained linkages. Journal of Engineering for Industry 91(1), 158–162 (1969)
Waldron, K.: Hybrid overconstrained linkages. Journal of Mechanisms 3(2), 73–78 (1968)
McCarthy, J.M.: Geometric Design of Linkages. Springer, New York (2000)
Dai, J.S., Huang, Z., Lipkin, H.: Mobility of overconstrained parallel mechanisms. ASME Journal of Mechanical Design 128(1), 220–229 (2006)
Adams, J.D., Whitney, D.E.: Application of screw theory to constraint analysis of mechanical assemblies joined by features. ASME Journal of Mechanical Design 123(1), 26–32 (2001)
Smith, D.: Constraint Analysis of Assemblies Using Screw Theory and Tolerance Sensitivities. MS Thesis, Brigham Young University, Provo, UT (2003)
Kong, X., Gosselin, C.M.: Type synthesis of 3-dof translational parallel manipulators based on screw theory. ASME Journal of Mechanical Design 126(1), 83–92 (2004)
Howell, L.L., Midha, A.: Parametric deflection approximations for end-loaded, large-deflection beams in compliant mechanisms. ASME Journal of Mechanical Design 117(1), 156–165 (1995)
Howell, L.L.: Compliant Mechanisms. Wiley-Interscience, New York (2001)
Su, H.-J., Dorozhkin, D.V., Vance, J.M.: A screw theory approach for the conceptual design of flexible joints for compliant mechanisms. ASME Journal of Mechanisms and Robotics 1(4), 041009 (2009)
Su, H.-J.: Mobility analysis of flexure mechanisms via screw algebra. ASME Journal of Mechanisms and Robotics 3(4), 041010 (2011)
Su, H.-J., Tari, H.: On line screw systems and their application to flexure synthesis. ASME Journal of Mechanisms and Robotics 3(1), 011009 (2011)
Su, H.-J., Tari, H.: Realizing orthogonal motions with wire flexures connected in parallel. ASME Journal of Mechanical Design 132(12), 121002 (2010)
Yu, J., Li, S., Su, H.J., Culpepper, M.L.: Screw theory based methodology for the deterministic type synthesis of flexure mechanisms. ASME Journal of Mechanisms and Robotics 3(3), 031008 (2011)
Bennett, G.: A new mechanism. Engineering 76 (1903)
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Su, HJ., Zhou, L., Zhang, Y. (2013). Mobility Analysis and Type Synthesis with Screw Theory: From Rigid Body Linkages to Compliant Mechanisms. In: Kumar, V., Schmiedeler, J., Sreenivasan, S., Su, HJ. (eds) Advances in Mechanisms, Robotics and Design Education and Research. Mechanisms and Machine Science, vol 14. Springer, Heidelberg. https://doi.org/10.1007/978-3-319-00398-6_6
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DOI: https://doi.org/10.1007/978-3-319-00398-6_6
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