3D-link dynamics simulator based on N-single particle movement

The purpose of this paper is to suggest new 3-D N-link system movement simulator. Previous presented method used to "Jacobian" matrix for connecting between the workspace coordination and the angle state space for representing the whole N-link system. But this system has difficulties for simulating the whole dynamics of the general N-link system from the side of computational cost and the precision of the calculations. The major reasons depend on the fundamental principle of conversion equivalence between the work space coordination x^→ and the angle state space q^→, this principle assure that we can change the work space coordinate into the angle state space coordinate which is convenient for the calculation, but this conversion have singularity that is, there is no inverse matrix of "J". In addition, there is accumulation of calculation error when it follows from the link root to link end in the case of calculating the multi-joint link movement dynamics, and the problem of treating the external force into the angular space dynamics. In this study, we consider the N-link system as N-particle movement system. And each of the particles is connected by a kind of spring damper model in imitation of a link. Because of this, our proposed method has no coordinate conversion between workspace and angular space in the dynamics simulation. And by the way of introducing some dynamics restriction, we can construct many of joint features such as fixed joint or single revolute joint, spherical link and so on. And we confirmed the 3D N-link system performance through some dynamics simulation such as walking, this simulator shows good accuracy and computational cost performances comparing previous proposed N-link system simulator.