### 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.

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