A Theoretical Dynamical Noninteracting Model for General Manipulation Systems Using Axiomatic Geometric Structures

Mercorelli, Paolo

doi:10.3390/axioms11070309

Cited by 3 publications

(2 citation statements)

References 40 publications

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“…Mercorelli, P. A Theoretical Dynamical Noninteracting Model for General Manipulation Systems Using Axiomatic Geometric Structures. [19] A new theoretical approach is developed to the study of robotics manipulators dynamics, based on the geometric approach to system dynamics, according to which some axiomatic definitions of geometric structures concerning invariant subspaces are used. 13.…”

Section: List Of Papers In Special Issuementioning

confidence: 99%

Henri Poincaré’s Comment on Calculus and Albert Einstein’s Comment on Entropy: Mathematical Physics on the Tenth Anniversary of Axioms

Haubold

2023

Axioms

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Section: List Of Papers In Special Issuementioning

confidence: 99%

Henri Poincaré’s Comment on Calculus and Albert Einstein’s Comment on Entropy: Mathematical Physics on the Tenth Anniversary of Axioms

Haubold

2023

Axioms

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“…The dynamic equation of this system can be obtained using the Euler-Lagrange approach and can be written as [17,18] M(ξ m ) ..…”

Section: Dynamic Equationmentioning

confidence: 99%

Contouring Control of a Five-Axis Machine Tool with Equivalent Errors

2022

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In this study, the contouring control problem of a five-axis machine tool was examined. Due to the rotation axes, there are two coordinate systems involved in the five-axis machine tool, namely the workpiece coordinate system and machine coordinate system. The five-axis machine tool is required to follow a given desired path with tool orientation specified in the workpiece coordinate system. However, the system dynamics of the machine tool is described in the machine coordinates. Kinematic transformations exist between the two coordinate systems. One challenge of the problem is to design a controller in the machine coordinate system that will meet the requirements in the workpiece coordinate system. Another challenge is to minimize both the position contour error and tool orientation error. The method of equivalent errors is adopted to design the contouring controller. The desired path and tool orientation in the workpiece coordinate system are transformed into a five-dimensional hyper-curve in the machine coordinate system. A contouring controller was designed to follow the five-dimensional hyper-curve using the method of equivalent errors. Both numerical and experimental results validate the effectiveness of the proposed contouring control method.

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A Full-Body Relative Orbital Motion of Spacecraft Using Dual Tensor Algebra and Dual Quaternions

Condurache

2023

Mathematics

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This paper proposes a new non-linear differential equation for the six degrees of freedom (6-DOF) relative rigid bodies motion. A representation theorem is provided for the 6-DOF differential equation of motion in the arbitrary non-inertial reference frame. The problem of the 6-DOF relative motion of two spacecraft in the specific case of Keplerian confocal orbits is proposed. The result is an analytical method without secular terms and singularities. Tensors dual algebra and dual quaternions play a fundamental role, with the solution representation being the relative problem. Furthermore, the representation theorems for the rotation and translation parts of the 6-DOF relative orbital motion problems are obtained.

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A Theoretical Dynamical Noninteracting Model for General Manipulation Systems Using Axiomatic Geometric Structures

Cited by 3 publications

References 40 publications

Henri Poincaré’s Comment on Calculus and Albert Einstein’s Comment on Entropy: Mathematical Physics on the Tenth Anniversary of Axioms

Henri Poincaré’s Comment on Calculus and Albert Einstein’s Comment on Entropy: Mathematical Physics on the Tenth Anniversary of Axioms

Contouring Control of a Five-Axis Machine Tool with Equivalent Errors

A Full-Body Relative Orbital Motion of Spacecraft Using Dual Tensor Algebra and Dual Quaternions

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