On MBS Constraints and Projections

Constraints in multibody systems are usually treated by a Lagrange I - method resulting in equations of motion together with the constraint forces. Going from non-minimal coordinates to minimal ones opens the possibility to project the original equations directly to the minimal ones, thus eliminating the constraint forces. The necessary procedure is described, a general example of combined machine-process dynamics discussed and a specific example given. For a n-link robot tracking a path the equations of motion are projected onto this path resulting in quadratic form linear differential equations. They define the space of allowed motion, which is generated by a polygon-system.

Deep Learning of (Periodic) Minimal Coordinates for Multibody Simulations

Mechanical systems are typically described through multi-body models with redundant coordinates, related by imposed constraints, where the dynamics is expressed with Differential Algebraic Equations. Alternatively, for rigid models, it may be preferable to employ minimal coordinates that do not require additional constraints, thus leading to Ordinary Differential Equations. However, to reduce a general multibody model to minimal coordinates and perform the simulation in the reduced space, the mapping between the minimal coordinates and the full coordinates is required. In this work, it is proposed to approximate such mapping using a neural network. In order to avoid overfitting and guarantee a continuous description of the solution manifold, the multibody dynamics information are included in the neural network training. The particular case where periodic minimal coordinates are required is treated and validated. In general, the methodology can be used when the mapping is unknown such as for spatial mechanisms with closed loops.

Evaluation and Experimental Validation of Efficient Simulation Models for Optimization of an Electrical Formula Car

This paper presents two different ways of modeling a road vehicle for general vehicle dynamics investigation and especially to optimize the suspension geometry. Therefore a numerically highly efficient model is sought such that it can be used later in gradient-based optimization of the suspension geometry. Based on a formula style vehicle with double wishbone suspension setup, a vehicle model based on ODE-formulation using a set of minimal coordinates is built up. The kinematic loops occurring in the double wishbone suspension setup are resolved analytically to a set of independent coordinates. A second vehicle model based on a redundant coordinate formulation is used to compare the efficiency and accuracy. The performance is evaluated and the accuracy is validated with measurement data from a real formula car.

SLIDING MODE CONTROL FOR PARALLEL ROBOTS DRIVEN BY ELECTRIC MOTORS IN TASK SPACE

This paper addresses the modelling of parallel robots including electric actuators. The dynamic model of the system is derived by applying the substructure method and Lagrangian equations with multipliers in form of redundant generalized coordinates. These equations are then transformed to the form of minimal coordinates of operational variables. Based on this form a sliding mode controller is designed for trajectory tracking in task space. Numerical simulations in MATLAB are carried out based on the 3RRR parallel robot in order to show the effectiveness of the proposal approach. The obtained results show a good behavior of the proposed task space tracking controller.

Forward dynamics of variable topology mechanisms—The case of constraint activation

Many mechanical systems exhibit changes in their kinematic topology altering the mobility. Ideal contact is the best known cause, but also stiction and controlled locking of parts of a mechanism lead to topology changes. The latter is becoming an important issue in human–machine interaction. Anticipating the dynamic behavior of variable topology mechanisms requires solving a nonsmooth dynamic problem. The core challenge is a physically meaningful transition condition at the topology switching events. Such a condition is presented in this article. Two versions are reported, one using projected motion equations in terms of redundant coordinates, and another one using the Voronets equations in terms of minimal coordinates. Their computational properties are discussed. Results are shown for joint locking of a planar 3R mechanisms and a 6DOF industrial manipulator.