On a new constraint equations form for alternative modeling the delta robot dynamics

Abstract

Mathematical modeling of the delta robot dynamics is significantly simplified due to the advanced consideration of the translational nature for the executive link motion. The rigorous derivation of the nonlinear geometric constraints equations is described in detail without the previously necessary consideration of the inverse problem of kinematics. The simplicity of the mathematical model of constraints obtaining is ensured by the introduction of only one angular variable for each kinematics chain instead of the traditionally used three. The proposed the constraint equations form, due to its simplicity, creates the possibility of differentiation over time in an analytical form with further analytical resolution regarding dependent velocities. That's why, in the general case, dependent velocities are excluded from consideration. The previously developed transition from the traditionally used Lagrange equations with constraints multipliers to multiplier-free vector-matrix equations in redundant coordinates reduces the mathematical model dimension on the geometric constraints double number.