Abstract
In this paper, we propose a forward kinematics model with natural coordinates for the Gough–Stewart manipulator and other spatial parallel mechanisms. The prevailing merits of this model are that the constraint equations are either quadratic or linear and the coordinates are fully Cartesian. As a result, the derivative matrix of the constraint equations only consists of linear or constant elements, which shows remarkable advantages in kinematic and dynamic analysis over those built through the rotation matrix, the elements of which often contain quadratic or transcendental functions. Application examples show that the virtues are obvious in the analysis of the kinematics of spatial parallel manipulators, especially for those with six full degrees of freedom (DoFs), including three translational DoFs and three rotational DoFs. In reality, this method is easily understood and will be widely used in engineering applications.
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References
Da Lioa M, Cossalter V, Lot R (2000) On the use of natural coordinates in optimal synthesis of mechanisms. Mech Mach Theory 35(10):1367–1389
García de Jalón J, Bayo E (1994) Kinematic and dynamic simulation of multibody sytems: the real-time challenge. Springer, Berlin Heidelberg New York
Hernández A, Altuzarra O, Avilés R, Petuya V (2003) Kinematic analysis of mechanisms via a velocity equation based in a geometric matrix. Mech Mach Theory 38(12):1413–1429
Szkodny Tadeusz (1995) Forward and inverse kinematics of IRb–6 manipulator. Mech Mach Theory 30(7):1039–1056
Ceccarelli M, Fino PMD, Jimenez JM (2002) Dynamic performance of caPaMan by numerical simulations. Mech Mach Theory 37(3):241–266
Szkodny T (1995) Dynamics of industrial robot manipulators. Mech Mach Theory 30(7):1057–1072
von Schwerin R (1999) Multibody system simulation–numerical methods, algorithms, and software. Springer, Berlin Heidelberg New York
Merlet J‐P (1993) Forward kinematics of nonpolyhedral parallel manipulators. J Mech Des 115:938–940
Husain M, Waldron KJ (1993) Position kinematics of a two limbed mixed mechanism. Mech Mach Theory 28(6):763–775
Gosselin CM, Merlet J‐P (1994) The direct kinematics of planar parallel manipulators: special architectures and number of solutions. Mech Mach Theory 29(8):1083–1097
Etemadi‐Zanganeh K, Angeles J (1995) Instantaneous kinematics of general hybrid parallel manipulators. J Mech Des 117:581–588
Tsai L‐W, Joshi S (2002) Kinematic analysis of 3–DoF position mechanisms for use in hybrid kinematic machines. J Mech Des 124:245–258
Merlet J–P (2004) Solving the forward kinematics of a gough-type parallel manipulator with interval analysis. Int J Rob Res 23(3):221–235
Miller K (2004) Optimal design and modeling of spatial parallel manipulators. Int J Rob Res 23(2):127–140
Ficher EF, Stewart A (1986) Platform-based manipulator: general theory and practical construction. Int J Rob Res 5(2):157–182
Jafari F, McInroy JE (2003) Orthogonal Gough‐Stewart platforms for micromanipulation. IEEE Trans Rob Autom 19(4)
Waldon KJ, Hunt KH (1991) Series–parallel dualities in actively coordinated mechanisms. Int J Rob Res 10(5):473–480
Kelley CT (1995) Iterative methods for linear and nonlinear equations, North Carolina State University. Society for Industrial and Applied Mathematics, Philadelphia
Zhao J‐S, Zhou K, Mao D‐Z, Gao Y‐F, Fang Y (2004) A new method to study the degree of freedom of spatial parallel mechanisms. Int J Adv Manuf Technol 3–4:288–294
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Zhao, J., Yun, Y., Wang, L. et al. Investigation of the forward kinematics of the Gough‐Stewart manipulator with natural coordinates. Int J Adv Manuf Technol 30, 700–716 (2006). https://doi.org/10.1007/s00170-005-0103-0
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DOI: https://doi.org/10.1007/s00170-005-0103-0