Curves of stationary acceleration according to alternative frame

Abstract

This paper investigates curves of stationary acceleration by using alternative frame which includes the principal normal vector, the derivative of principal normal vector and the Darboux vector. Mentioned curves are studied by the way of rigid body motions, that is to say a point in the moving body follows the curve and the alternative frame in the moving body stays aligned with the members of frame. It is determined that in which condition this special motion becomes to stationary acceleration motion. The matrix representations of a constant vector related to velocity vector of the motion which is used to characterize stationary acceleration is obtained by means of alternative frame curvatures. Some examinations are developed with some solutions of differential equations. The main result is attained as: general helix curves with linear curvature and torsion functions are curves of stationary acceleration which are curves in the rigid body motions group SE(3) correlated with robotics. The paths designed as stationary acceleration curves can lead the way to control the end-effectors of robots. Finally, some explanatory examples are imputed.