Dynamics solution of n-DOF global machinery model

Automated model generation and solution for motion planning and re-planning of automated systems will play an important role in future reconfigurable manufacturing systems (RMS). An n-DOF Global Kinematic Model (n-GKM) was previously developed for any combination of either rotational or translational type of joints. In this paper, the automatic generation of the dynamic equations for the n-GKM is presented. For the symbolic calculation of the n-GKM dynamic equations, the recursive Newton–Euler algorithm is employed using the symbolic algebra package MAPLE 12. The dynamic model is named Global Dynamic Model (n-GDM). The significance of the n-GDM is that it automatically generates each element of the inertia matrix A, Coriolis torque matrix B, centrifugal torque matrix C, and the gravity torque vector G, using Automatic Separation Method (ASM). The n-GDM is a dynamic solver for the n-GKM which includes predefined reconfigurable parameters. These parameters are used to control the joint's positive directions and its type (rotational and/or translational). Instead of solving the dynamics of different kinematic structures, the n-GDM can be used to auto-generate the solution by only defining these reconfigurable parameters. Using n-DOF Global Dynamic Model equations, a 3-DOF Global Dynamic Model (GDM) is derived. The 3-GDM has been validated using five selected cases (RR, RT, TR, TT planar and SCARA configurations). The results show the model ability to automatically generate different dynamic realizations for any required configuration.

► The dynamic equations for the n-DOF Global Kinematic Model are automatically generated. ► The Automatic Separation Method has been used for the symbolic calculation of the equations. ► The dynamic and kinematic models include combined rotational and/or translational joints. ► A 3-DOF Global Dynamic Model (GDM) is derived using the presented methodology. ► The 3-GDM has been validated using RR, RT, TR, TT and SCARA configurations.