Abstract
This chapter presents fundamental concepts, expressions, operations, and properties of FIS theory. Firstly, the finite screw in quasi-vector form and its composition operation, i.e., the screw triangle product, is derived from dual quaternion for the first time.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Sun T, Yang SF, Huang T et al (2017) A way of relating instantaneous and finite screws based on the screw triangle product. Mech Mach Theory 108:75–82
Sun T, Yang SF, Huang T et al (2018) A finite and instantaneous screw based approach for topology design and kinematic analysis of 5-axis parallel kinematic machines. Chin J Mech Eng 31:44
Sun T, Yang SF (2019) An approach to formulate the Hessian matrix for dynamic control of parallel robots. IEEE-ASME Trans Mechatron 24(1):271–281
Sun T, Song YM, Gao H et al (2015) Topology synthesis of a 1-translational and 3-rotational parallel manipulator with an articulated traveling plate. J Mech Rob Trans ASME 7(3):031015
Yang SF, Sun T, Huang T et al (2016) A finite screw approach to type synthesis of three-DOF translational parallel mechanisms. Mech Mach Theory 104:405–419
Sun T, Huo XM (2018) Type synthesis of 1T2R parallel mechanisms with parasitic motions. Mech Mach Theory 128:412–428
Sun T, Song YM, Li YG et al (2010) Workspace decomposition based dimensional synthesis of a novel hybrid reconfigurable robot. J Mech Rob Trans ASME 2(3):031009
Sun T, Song YM, Dong G et al (2012) Optimal design of a parallel mechanism with three rotational degrees of freedom. Rob Comput Integr Manuf 28(4):500–508
Sun T, Liang D, Song YM (2018) Singular-perturbation-based nonlinear hybrid control of redundant parallel robot. IEEE Trans Industr Electron 65(4):3326–3336
Sun T, Lian BB, Song YM et al (2019) Elastodynamic optimization of a 5-DoF parallel kinematic machine considering parameter uncertainty. IEEE ASME Trans Mechatron 24(1):315–325
Ball RS (1900) A treatise on the theory of screws. Cambridge University Press, Cambridge
McCarthy JM, Soh GS (2011) Geometric design of linkages, 2nd edn. Springer, New York
Hunt KH, Parkin IA (1995) Finite displacements of points, planes, and lines via screw theory. Mech Mach Theory 30(2):177–192
Huang C, Chen CM (1995) The linear representation of the screw triangle—a unification of finite and infinitesimal kinematics. J Mech Des Trans ASME 117(4):554–560
Hervé JM (1999) The Lie group of rigid body displacements, a fundamental tool for mechanism design. Mech Mach Theory 34(5):719–730
Ceccarelli M (2000) Screw axis defined by Giulio Mozzi in 1763 and early studies on helicoidal motion. Mech Mach Theory 35(6):761–770
Tsai LW (1999) Robot analysis: the mechanics of serial and parallel manipulators. Wiley, New York
Huang Z, Li QC, Ding HF (2013) Theory of parallel mechanisms. Springer, Berlin
Meng J, Liu GF, Li ZX (2007) A geometric theory for analysis and synthesis of sub-6 DoF parallel manipulators. IEEE Trans Rob 23(4):625–649
Murray RM, Li ZX, Sastry SS (1994) A mathematical introduction to robotic manipulation. CRC Press, Boca Raton
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
Copyright information
© 2020 Springer Nature Singapore Pte Ltd.
About this chapter
Cite this chapter
Sun, T., Yang, S., Lian, B. (2020). Finite and Instantaneous Screw Theory. In: Finite and Instantaneous Screw Theory in Robotic Mechanism. Springer Tracts in Mechanical Engineering. Springer, Singapore. https://doi.org/10.1007/978-981-15-1944-4_2
Download citation
DOI: https://doi.org/10.1007/978-981-15-1944-4_2
Published:
Publisher Name: Springer, Singapore
Print ISBN: 978-981-15-1943-7
Online ISBN: 978-981-15-1944-4
eBook Packages: Intelligent Technologies and RoboticsIntelligent Technologies and Robotics (R0)