Multi-Contact Friction Dynamics Using Tangential Reaction Impulses
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Solution Overview
Problem
Current discrete mechanical systems face challenges in accurately modeling and predicting the motion of objects with multiple contacts, particularly in real-time applications, due to the complexity of frictional interactions, which affects the accuracy and speed of rigid-body dynamics simulations.
Innovation Solution
A computer-implemented method that computes generalized forces and reaction impulses by associating each contact with a friction cone, constraining the tangential reaction to be orthogonal to the normal reaction and minimizing energy over an interval, allowing for the determination of end-of-interval positions and velocities of objects with multiple contacts.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If frictional interactions are modeled in detail for multi-contact systems, then accuracy of motion prediction is improved, but computational complexity increases
Solution Approach 1:
The frictional contact forces are segmented into normal and tangential components, with each contact point handled separately through friction cones. This segmentation allows the complex multi-contact problem to be decomposed into manageable sub-problems that can be solved systematically while maintaining accuracy.
Solution Approach 2:
The patent introduces friction cones in impulse space, adding a dimensional framework for representing frictional constraints. By formulating the problem in terms of impulse vectors within conic constraints rather than traditional force equations, the method transforms the computational structure to enable efficient solution of multi-contact friction problems.
2Speed
If real-time computation is required for rigid-body dynamics, then speed of computation is improved, but accuracy of friction modeling deteriorates
Solution Approach 1:
The method pre-defines friction cones for each contact point based on Coulomb friction criteria before solving the dynamics problem. By establishing these conic constraints in advance, the computationally intensive friction modeling is prepared beforehand, allowing real-time solution of the motion equations without sacrificing frictional accuracy.
Solution Approach 2:
The patent replaces traditional continuous friction force modeling with discrete impulse-based formulations constrained by friction cones. This substitution transforms the differential equations of motion with continuous friction terms into algebraic equations with conic constraints, enabling real-time computation while preserving essential friction effects.
Data Source
AI summary
In a mechanical system with an object having a set of two or more contacts, methods are disclosed for determining object motion by computing the tangential generalized reaction impulse and force. The methods includes receiving input values that include an initial generalized position and an initial generalized velocity of the object at time t, and computing a generalized force. The methods further includes computing, respectively for the reaction impulse and force: a generalized reaction impulse and force, and a tangential generalized reaction impulse and force. The methods use the tangential generalized reaction impulse and force to, respectively, compute an end-of-interval generalized position and velocity, and a generalized acceleration, which are output for use by an application.