Kinematic and dynamic modeling of spherical joints using exponential coordinates
- Kinematic and dynamic modeling of spherical joints using exponential coordinates
- 김진욱; Sung-Hee Lee; Frank C Park
- Exponential coordinates; spherical joint; rotation; parallel mechanism
- Issue Date
- Proceedings of the Institution of Mechanical Engineers. Part C, Mechanical engineering science
- VOL 228, NO 10, 1777-1785
- Traditional Euler angle-based methods for the kinematic and dynamic modeling of spherical joints involve highly complicated formulas that are numerically sensitive, with complex bookkeeping near local coordinate singularities. In this regard, exponential coordinates are known to possess several advantages over Euler angle representations. This paper presents several new exponential coordinate-based formulas and computational procedures that are particularly useful in the modeling of mechanisms containing spherical joints. Computationally robust procedures are
derived for evaluating the forward and inverse formulas for the angular velocity and angular acceleration in terms of exponential coordinates. We show that these formulas simplify the parametrization of joint range limits for spherical joints, and lead to more compact equations in the forward and inverse dynamic analysis of mechanisms containing spherical joints.
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