Computer-aided analysis of mechanical systems
Computer-aided analysis of mechanical systems
Computation of the solutions of nonlinear polynomial systems
Computer Aided Geometric Design
Box-bisection for solving second-degree systems and the problem of clustering
ACM Transactions on Mathematical Software (TOMS)
Robot Analysis and Design: The Mechanics of Serial and Parallel Manipulators
Robot Analysis and Design: The Mechanics of Serial and Parallel Manipulators
Kinematic and Dynamic Simulation of Multibody Systems: The Real Time Challenge
Kinematic and Dynamic Simulation of Multibody Systems: The Real Time Challenge
Rigorous Lower and Upper Bounds in Linear Programming
SIAM Journal on Optimization
Safe bounds in linear and mixed-integer linear programming
Mathematical Programming: Series A and B
Efficient and Safe Global Constraints for Handling Numerical Constraint Systems
SIAM Journal on Numerical Analysis
Graphs and Digraphs, Fourth Edition
Graphs and Digraphs, Fourth Edition
Towards more efficient interval analysis: corner forms and a remainder interval newton method
Towards more efficient interval analysis: corner forms and a remainder interval newton method
A branch-and-prune solver for distance constraints
IEEE Transactions on Robotics
A Relational Positioning Methodology for Robot Task Specification and Execution
IEEE Transactions on Robotics
Synthesizing grasp configurations with specified contact regions
International Journal of Robotics Research
Randomized path planning on manifolds based on higher-dimensional continuation
International Journal of Robotics Research
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This paper presents a new method to isolate all configurations that a multiloop linkage can adopt. The problem is tackled by means of formulation and resolution techniques that fit particularly well together. The adopted formulation yields a system of simple equations (only containing linear, bilinear, and quadratic monomials, and trivial trigonometric terms for the helical pair only) whose structure is later exploited by a branch-and-prune method based on linear relaxations. The method is general, as it can be applied to linkages with single or multiple loops with arbitrary topology, involving lower pairs of any kind, and complete, as all possible solutions get accurately bounded, irrespective of whether the linkage is rigid or mobile.