Study of the hexapod dynamics using equations in redundant coordinates

Abstract

The dynamics of hexapods (Stewart platforms) has been extensively studied for several decades. In this problem, the equations of motion are usually constructed using the basic theorems of mechanics. Lagrange equations of the second kind are often constructed for the same purpose. In the present paper, a new form of dynamic equations is considered. These equations are a special form of equations of motion of a system of rigid bodies (equations of dynamics in redundant coordinates). This approach is used to obtain the differential equations of motion of a hexapod in redundant coordinates. In this case, the loaded Stewart platform is considered as a rigid body, whose position is determined by setting the radius vector of the center of mass and the unit vectors of the body-axes system. From the vector form of the Lagrange equations of the first kind scalar differential equations of motion of the mechanical system under consideration are obtained. The obtained equations for some standard motions of the hexapod are numerically integrated. It is noted that the stable motion of the mechanical system under consideration can be obtained only with the introduction of feedbacks.