KINEMATIC AND DYNAMIC ANALYSIS OF MULTIBODY SYSTEMS USING THE KRONECKER PRODUCT

Nguyen Thai Minh Tuan, Chung Thanh Pham, Do Dang Khoa, Phan Dang Phong

Abstract


This paper employ Khang’s definition of the partial derivative of a matrix with respect to a vector and the Kronecker product to define translational and rotational Hessian matrices. With these definitions, the generalized velocities in the expression of a linear acceleration or an angular acceleration are collected into a quadratic term. The relations of Jacobian and Hessian matrices in relative motion are then established. A new matrix form of Lagrange’s equations showing clearly the quadratic term of generalized velocities is also introduced.


Keywords


Jacobian matrix; Hessian matrix; Kronecker product; velocity-free Coriolis matrix; matrix form of Lagrange’s equations

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References


Zhao Tieshi, et al. - Kinematics and Dynamics Hessian Matrices of Manipulators Based on Screw Theory, Chin. J. Mech. Eng., 28 (2015) 226-235.

Wen-Hua D., et al. - Control-orientated dynamic modeling of forging manipulators with multi-closed kinematic chains, Robotics and Computer-Integrated Manufacturing, 30 (5) (2014) 421-431.

Nguyen Van Khang - Consistent definition of partial derivatives of matrix functions in dynamics of mechanical systems, Mechanism and Machine Theory, 45 (2010) 981-988.

Nguyen Van Khang - Kronecker product and a new matrix form of Lagrangian equations with multipliers for constrained multibody systems, Mechanics Research Communications, 38 (2011) 294-299.

Fuzhen Z. - Matrix Theory: Basic Results and Techniques, Springer New York, 2011, pp. 399.

Brewer J. - Kronecker products and matrix calculus in system theory, IEEE Transactions on Circuits and Systems, 25 (9) (1978) 772-781.

Laub A.J. - Matrix Analysis for Scientists and Engineers, SIAM, 2005, pp. 157.

Nguyen Van Khang - Dynamics of Multibody Systems, (second printing with some corrections and additions) (in Vietnamese). Hanoi Science and Technics Publishing House, 2017.

Schiehlen W. and Eberhard P. - Applied Dynamics (Vol. 57), Springer, 2014, pp. 215.




DOI: https://doi.org/10.15625/2525-2518/57/1/12285

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