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 mo-
tion 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 differen-
tial 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.