Kinematic-geometry of a line trajectory and the invariants of the axodes
Yanlin Li, Fatemah Mofarreh, Rashad A. Abdel-Baky
Abstract
Abstract In this article, we investigate the relationships between the instantaneous invariants of a one-parameter spatial movement and the local invariants of the axodes. Specifically, we provide new proofs for the Euler-Savary and Disteli formulas using the E. Study map in spatial kinematics, showcasing its elegance and efficiency. In addition, we introduce two line congruences and thoroughly analyze their spatial equivalence. Our findings contribute to a deeper understanding of the interplay between spatial movements and axodes, with potential applications in fields such as robotics and mechanical engineering.
Topics & Concepts
KinematicsMathematicsMathematical proofEleganceEquivalence (formal languages)Congruence relationGeometryTrajectoryLine (geometry)RoboticsAlgebra over a fieldPure mathematicsArtificial intelligenceComputer scienceRobotClassical mechanicsAestheticsPhysicsAstronomyPhilosophyMathematics and ApplicationsPoint processes and geometric inequalitiesAdvanced Differential Geometry Research