A new formulation for the dynamics of rigid bodies with unilateral interactions

IF 4.5 1区 工程技术 Q1 ENGINEERING, MECHANICAL Mechanism and Machine Theory Pub Date : 2024-10-15 DOI:10.1016/j.mechmachtheory.2024.105809
David M. Solanillas Francés, József Kövecses
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Abstract

A new approach is introduced for modelling multibody systems with unilateral interactions. We focus on the simulation of the forward dynamics problem. The dynamic and kinematic steps are solved with two different formulations. First, a four-point-mass model is used to represent the rigid body dynamics, avoiding the use of rotational coordinates. Therefore, the nonlinear inertial terms do not appear explicitly in the formulation. However, there are constant distance constraints between the point masses. The velocities of the point masses are obtained by solving the dynamics with this model. The angular velocity of the rigid body can be calculated from such velocities. Then, the kinematic problem is solved using the rigid body representation that fully embeds the constant distance constraints. Thus, the proposed approach can improve the accuracy of the dynamic problem with unilateral contact since the nonlinear inertial terms do not enter the formulation explicitly. The constraints appear explicitly in the dynamics representation, but they are linear there. In the position update, they are embedded exactly through the model change back to the angular velocity-based minimum coordinate formulation.
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具有单边相互作用的刚体动力学新公式
我们引入了一种新方法来模拟具有单边相互作用的多体系统。我们的重点是模拟前向动力学问题。动力学和运动学步骤采用两种不同的公式进行求解。首先,使用四点质量模型表示刚体动力学,避免使用旋转坐标。因此,非线性惯性项并没有明确出现在公式中。不过,点质量之间存在恒定距离约束。点质量的速度可通过使用该模型进行动力学求解获得。刚体的角速度可以根据这些速度计算出来。然后,使用完全包含恒定距离约束的刚体表示法来解决运动学问题。因此,由于非线性惯性项不会明确进入公式,因此建议的方法可以提高单侧接触动态问题的精度。这些约束条件明确出现在动力学表征中,但它们是线性的。在位置更新中,它们通过模型变化准确地嵌入到基于角速度的最小坐标表述中。
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来源期刊
Mechanism and Machine Theory
Mechanism and Machine Theory 工程技术-工程:机械
CiteScore
9.90
自引率
23.10%
发文量
450
审稿时长
20 days
期刊介绍: Mechanism and Machine Theory provides a medium of communication between engineers and scientists engaged in research and development within the fields of knowledge embraced by IFToMM, the International Federation for the Promotion of Mechanism and Machine Science, therefore affiliated with IFToMM as its official research journal. The main topics are: Design Theory and Methodology; Haptics and Human-Machine-Interfaces; Robotics, Mechatronics and Micro-Machines; Mechanisms, Mechanical Transmissions and Machines; Kinematics, Dynamics, and Control of Mechanical Systems; Applications to Bioengineering and Molecular Chemistry
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