An efficient method for obtaining the general solution for the force balance equations with hard point contacts.

Area of Science:

• Robotics and Mechanical Systems
• Computational Mechanics
• Multibody Dynamics

Background:

• Traditional pseudoinverse formulations for solving force balance equations can be computationally intensive.
• Efficiently obtaining general solutions for force balance equations is critical in robotics and mechanical system analysis.
• Handling hard point contacts requires robust and optimized computational methods.

Purpose of the Study:

• To present a compact formulation for solving force balance equations that is more efficient than traditional methods.
• To reduce the computational time required for obtaining the general solution of force balance equations.
• To enhance the parallelism of algorithms used in contact mechanics.

Main Methods:

• Decomposition of force balance equations into two sets of smaller, rank 3 linear equations.
• Strategic selection of coordinate frames for the reference member and contact points.
• Application of a compact formulation combined with equation decomposition.

Main Results:

• Reduced steps in the Gaussian elimination process.
• Increased parallelism in the computational algorithm.
• Minimized computation time for solving force balance equations with hard point contacts.

Conclusions:

• The presented compact formulation and decomposition method offer significant efficiency gains over traditional approaches.
• This method is particularly effective for problems involving hard point contacts.
• The enhanced computational efficiency and parallelism have implications for real-time applications in robotics and mechanics.