The Kinematics of a New Schönflies Motion Generator Parallel Manipulator Using Screw Theory

Jaime Gallardo-Alvarado, Horacio Orozco-Mendoza, Ramon Rodriguez-Castro, Alvaro Sanchez-Rodriguez and Luis A. Alcaraz-Caracheo ()
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Jaime Gallardo-Alvarado: Department of Mechanical Engineering, National Technological Institute of Mexico, Celaya Campus, Celaya 38010, Mexico
Horacio Orozco-Mendoza: Department of Mechanical Engineering, National Technological Institute of Mexico, Celaya Campus, Celaya 38010, Mexico
Ramon Rodriguez-Castro: Department of Mechanical Engineering, National Technological Institute of Mexico, Celaya Campus, Celaya 38010, Mexico
Alvaro Sanchez-Rodriguez: Department of Mechanical Engineering, National Technological Institute of Mexico, Celaya Campus, Celaya 38010, Mexico
Luis A. Alcaraz-Caracheo: Department of Mechanical Engineering, National Technological Institute of Mexico, Celaya Campus, Celaya 38010, Mexico

Mathematics, 2025, vol. 13, issue 14, 1-25

Abstract: In this work, an innovative Schönflies motion generator manipulator is introduced, featuring a parallel architecture composed of serial chains with mixed degrees of freedom. Fundamental kinematic aspects essential to any manipulator such as displacement, velocity, acceleration, and singularity analyses are thoroughly addressed. Screw theory is employed to derive compact input–output expressions for velocity and acceleration, leveraging the properties of reciprocal screws and lines associated with the constrained degrees of freedom in the parallel manipulator. A key advantage of the proposed design is its near-complete avoidance of singular configurations, which significantly enhances its applicability in robotic manipulation. Numerical examples are provided to validate the theoretical results, with corroboration from specialized tools such as ADAMS™ software and data fitting algorithms. These results confirm the reliability and robustness of the developed kinematic analysis approach.

Keywords: Schönflies motion; parallel manipulator; screw theory; kinematics (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
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