Session 10C: Mechanical Systems Modelling

Title: Object-oriented modelling of a flexible beam including geometric nonlinearities
Authors: Davide Invernizzi, Bruno Scaglioni, Gianni Ferretti and Paolo Albertelli
Abstract:In this paper, an efficient approach for the modelling and simulation of slender beams subject to heavy inertial loads is presented. The limitations imposed by a linear formulation of elasticity are overcome by a second order expansion of the displacement field, based on a geometrical exact beam model. In light of this, the nonlinearities of the elastic terms are shifted as inertial contributions, which yields an expression of the equations of motion in closed form. Thanks to the formulation in closed form, the proposed model is implemented in Modelica, with particular care to the suitability of the model with respect to the Modelica Multibody library. After describing the model formulation and implementation, the paper presents some simulation results, in order to validate the model with respect to benchmarks, widely adopted in literature.
Links: Full paper

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Title: Musculoskeletal Modeling of the Hand and Contact Object in Modelica
Authors: Shashank Swaminathan and Johan Andreasson
Abstract:The paper's primary goal is to develop a mathematical model that could be used towards the development and improvement of orthotic assist gloves. The model is constructed using component based modeling in the object-oriented declarative language Modelica, specifically the MultiBody Modelica library. Multiple hand models currently do exist; however, they are mainly causal, and require separate development and validation of mathematical solvers before use. By using Modelica, the model is constructed from the system’s physical equations, thereby relieving issues regarding validity of the model’s computational equations; the acausality inherent in Modelica allows for more model development that more closely mirrors relations in the physical world. The model is scoped to be able to model the kinematics and dynamics of the hand when grasping a spherical object – both bone structure and muscle geometry and actuation are simplifications based off anatomy literature. The contact model is developed as a separate component from the hand system. The main design goal of the contact model is to represent the characteristics of a relatively rigid object that still maintains a degree of friction and pliability on the surface layer. The main two grasps tested in the paper are the prehensile and precision grasps (powerful and dexterous grasps). The muscle actuation profiles per each finger are adjusted until the desired dynamic profile is achieved for each type of grasp. The main data points of interests are the joint angles and contact forces for each finger. Further validation of the model is done using the animation automatically generated by the tool. Testing results indicate that the model can successfully simulate contractions at all levels of abstraction of the hand’s components (basic bone-joint components, finger components, and the overall hand system). The results also indicate that both prehensile and precision grasps are possible, given appropriate muscle actuation and finger orientation parameter values.
Links: Full paper

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Title: Modelica Spur Gears with Hertzian Contact Forces
Authors: Markus Dahl, Håkan Wettergren and Henrik Tidefelt
Abstract:To be able to capture the dynamics of entire systems is one of the strengths of the Modelica language. This article will examine the possibility of modeling spur gears in the Modelica environment Wolfram SystemModeler, and integrating them with other rotating machinery elements, such as roller bearings and flexible shafts. The contact forces between spur gears are based on the Hertzian Theory of Contact.
Links: Full paper

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Title: Modeling of Roller Bearings
Authors: Tobias Weiser and Burkhard Corves
Abstract:Modeling of multibody mechanics plays a central role in the design of mechatronic systems. Roller Bearings contribute stiffness and damping to the system dynamics of a mechatronic system. This article shows the stiffness modeling of a few roller bearing types. The kinematics of deformation of a roller bearing are shown. Based on the principle of Hertz contact stress the elastic forces and torques are calculated. These forces are considered and implemented in the Multi-Body-System Library.
Links: Full paper