IUTAM Symposium on Intelligent Multibody Systems – Dynamics, Control, Simulation

Multibody modelling involves taking fundamental decisions during the multibody model construction that not only condition its validity for the particular application foreseen but also have fundamental implications on the suitability of the numerical methods used on its analysis. The decision on allowing a particular flexible body to exhibit linear or nonlinear deformations or even to consider it part of the multibody system or as a structural component with which the system interacts is a crucial part of the modeling process. The description of the kinematic relations between moving components can be represented by perfect kinematic constraints or by contact pairs, as when local effects in the joints, generally associated with deviations from nominal conditions or to functional features, must be considered. The interaction of the multibody model with the ‘environment’ may require a substantial modelling effort that involves decisions on geometric description of features, on contact mechanics or even on numerical methodologies to handle co-simulation of systems with equilibrium equations that are solved with different numerical methods. Several areas are transversal to all the challenges identified and discussed here. The suitability of the numerical time integrators not only to handle the multibody model assumptions but also their interaction with other systems are of fundamental importance in the correct solution of the system dynamics. Descriptive and differential geometry also plays a very important role not only in the description of the relative kinematics of the systems but also in the modelling of the interactions.

This paper describes the role played by skeletal and musculo-skeletal modeling and analysis in: (i) the customization of low-cost active knee-ankle-foot orthoses aimed at assisting the gait of spinal-cord-injured subjects possessing some level of hip actuation; (ii) the adaptation process of the patients to the devices. It is shown that personalized multibody-based human models and related methods and techniques are very helpful for motor-gearbox selection and swing motion definition, for monitoring progress during the training sessions, for evaluating the final outcome provided by the assistive devices, and for anticipating their long-term impact on the patient’s health.

Optimal Control methods are increasingly used for the control of multibody systems (MBS). This work analyzes the different dynamic formulations and compare their performances in solving Optimal Control Problem. The focus is on minimal coordinates and the derivation of the dynamics via the recursive methods for tree-like MBS (i.e., the so-called Newton-Euler and Order-N recursive algorithms). The different formulations are introduced and their derivations are discussed. A benchmark case study (i.e., a 3D series manipulator balancing an inverted pendulum) is modeled and a series of manipulation tasks (movement of the end effector in the 3D space) are performed. The OCP is formulated and solved with the help of the CasADi software while the dynamic formulations are generated by the Robotran software. Results show that the implicit and semi-explicit formulations derived via the Newton-Euler recursive algorithm lead to faster computation of the OCP than the explicit formulations. This is explained by a more compact expression for the implicit dynamics. However, a lower number of high local minima is observed with the explicit formulations for the most extreme robot manipulations.

In this chapter, a novel procedure for inverse dynamics modeling of flexible multibody systems using a driving constraints approach in the form of a forward dynamics analysis is presented. The flexible 3RPR parallel manipulator is chosen here as a flexible multibody system with closed kinematic chains to introduce this approach. The equations of motion are derived using the floating frame of reference formulation. Assuming a prescribed trajectory of the end-effector, the generalized coordinates of the rigid manipulator associated with the prismatic and revolute joints are obtained from an inverse kinematics analysis of the manipulator. This solution is further exploited in a forward dynamics analysis of the flexible manipulator to form the required driving constraints for obtaining the approximate values of the actuating forces and torques. Finally, the inverse dynamics analysis of the flexible manipulator is carried out by including some additional driving constraints associated with the generalized elastic coordinates to obtain the high-accuracy approximate values of the actuating forces and torques for tracking the prescribed trajectory by the end-effector. To numerically validate the approach, the obtained actuating forces and torques are applied to the simulated flexible manipulator to check the final trajectory of the end-effector. The results confirm the accuracy of the proposed approach.

The probabilistic solutions of elastic stretched beams are studied when the beam is discretized by finite difference scheme and excited by Gaussian white noise which is fully correlated in space. The nonlinear multi-degree-of-freedom system about the random vibration of stretched beam is formulated by finite difference scheme first. Then the relevant Fokker-Planck-Kolmogorov equation is solved for the probabilistic solutions of the system by the state-space-split and exponential polynomial closure method. Monte Carlo simulation method and equivalent linearization method are also adopted to analyze the probabilistic solutions of the system responses, respectively. Numerical results obtained with the three methods are presented and compared to show the computational efficiency and numerical accuracy of solving the Fokker-Planck-Kolmogorov equation by the state-space-split and exponential polynomial closure method in analyzing the probabilistic solutions of the beams discretized by finite difference scheme and excited by Gaussian white noise. The techniques of using the state-space-split procedure for dimension reduction of the beam systems are discussed through the given beam systems with different space distributions of excitations.

This paper deals with the dynamical modeling of flexible multibody systems like elastic robots that go in contact with the environment. Models for elastic systems have a large degree of freedom leading to longer calculation times for solving the equations of motion (EOM). Conventionally, this includes the inversion of the mass matrix with a cubic run time complexity O(n ³). By using a subsystem formulation and the Projection Equation an O(n) algorithm can be formulated that significantly reduces the simulation time. Additional contacts with the environment can be included in the equations of motion by the corresponding constraint Jacobian and the contact forces. For the explicit calculation of these forces, normally the inverse of the mass matrix is needed again. A novel algorithm to avoid this inversion is presented. Therein, the contact forces are calculated by additional runs of the same O(n) algorithm that is used without contact. The transition phase between different contact states is treated with the help of Newton’s impact law, again avoiding the inversion of the mass matrix. Simulation results for an elastic robot show the effectiveness of the proposed algorithms.

The deployment of continuum robotic surfaces has strong potential over a wide range of engineering disciplines. To allow such compliant, actively actuated surfaces to be controlled accurately and efficiently, reliable kinematic and dynamic models are required. The main challenge appears when the continuum surfaces become very flexible and undergo large deformations, an issue which is little studied in continuum robotics to date. This paper tackles this problem through the application of a lumped-mass approach for analysis of continuum surfaces that are subject to large deformations due to either gravity or external loading applied by representative flexible actuators. The developed model describes the surface kinematics by providing a means of solving for the displacement profile across the surface. The model takes into account all the essential factors such as gravitational effects, material properties of a flexible plate, inertial forces, material damping, and in-depth shear effects across the surface. An experimental setup has been developed to test an actuated flexible surface under different boundary conditions, with results showing mean percentage error of 4.8% at measured surface points.

The presented work covers the definition of three different methods for designing orthoses produced by the methods of rapid prototyping of polymer structures. The stages of design and production of orthoses are defined. The methods are illustrated, by way of example, of an orthosis for upper limb fracture. The use of parametric modeling facilitates easier and faster preparation of CAD models. In the production of orthoses, the use of an automated approach by adapting a parametric model leads to a number of advantages. Besides shortening the required workflow time, there are opportunities to track the effectiveness and performance of the end products and adjust the relevant parametric models in the catalog in order to improve them and embed the resulting know-how in the model. The creation of a workflow to facilitate easier CAD modeling in combination with reverse engineering technology and rapid prototyping technologies offers excellent opportunities to improve the resulting orthoses for the patients in need.

This paper discusses a general procedure for creating a computer-aided design (CAD) model of an existing commercial sheep hair shearing device for simulation purpose. In this paper, simulation was carried out using the commercial software RecurDyn while the CAD models of the components of the device were created using SolidWorks software. Note that the mechanism in the device can be identified as an RCCR spatial four-bar linkage which was also modeled analytically from its kinematics point of view. The dynamic equations of motion were developed using the concept of the cut-joint approach and the Decoupled Natural Orthogonal Complement (DeNOC) matrices. The equations of motion were then used to simulate the mechanism in Matlab environment. The results were compared to those obtained using the CAD model in RecurDyn environment.

The motivation for this work is to model the seismic response of a structure taking into account the base three Earth components (seismic source, wave path and local soil profile) plus the engineering structure at the end of the line and modelling all of them in one system. The main aim is to develop an efficient hybrid hi-performance methodology and software that model the dynamic response of structures during earthquake accounting for the main characteristics and mechanical properties of the soil and seismic source, plus the specific structural peculiarities and mechanical behavior of the building/underground structure. The present study investigates the soil-foundation-structure interaction and the influence of the structural dynamics over the whole system’s motion. The boundary integral equation method (BIEM) is applied to model the semi-infinite part of the geological domain, while the finite soil profile is described via finite element method (FEM). The structural dynamics is simulated using finite elements in absolute coordinates (FEAC), which allows the geometrical nonlinearity in dynamic behavior of the engineering structure to be taken into account. Example of forced motion of the rigid foundation as a result of wave propagation overlapped by a four stroke structural displacements illustrates the efficiency of the hybrid model.