Abstract: Aiming at the problem of complex process and large amount of calculation for the constraint force of parallel mechanism, the Delta parallel mechanism was taken as an example to make theoretical derivation, simulation analysis and experimental verification of its constraining force formula. First, Lagrange dynamics model of Delta parallel mechanism was established. The second-order influence coefficient matrix was used to establish the acceleration mathematical model of the driving slider. Then the force analysis of the driving slider was carried out to obtain the constraint force equation. The constraint force equation was solved with MATLAB and its correctness was verified with ADAMS. The binding time curve of the ball hinge of the driving slider was obtained. Finally, the acceleration and vertical constraint data of the driving slider were obtained with Delta parallel mechanism and gyroscope. The experiment results show that the analysis of constraint force and simulation of the Delta parallel mechanism based on Lagrange equation and secondorder influence coefficient matrix can not only get the correct constraint analysis result, simplify the analysis process, obtain a relatively standard and concise constraint equation of ball hinge, but also greatly reduce the complexity of derivation. Moreover, it can be extended to other parallel mechanism and provide a new method for binding analysis of parallel mechanism.

Key words:  parallel mechanism; dynamics analysis; constraint force; Lagrange equation; influence coefficient matrix