Nonlinear regular dynamics of a single-degree robot model

SUMMARYThis paper presents a mathematical model of a robot with one degree of freedom and numerical investigation of its dynamics in a particular parameter scan which is close to the upper boundary of the estimates for the parameters of rigidity and friction, while the length parameter L is treated as a free control parameter. In this L-scan the quasiperiodic and frequency locked solutions, their pattern and order of appearance are studied in the interval from the parameter range of immediate engineering significance to the point of appearance of transient chaos. In particular, a fractaltype multiple splitting of Arnold tongues is found in the parameter region bordering the range of engineering significance.

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Nonlinear dynamics of a single-degree robot model Part 2: Onset of chaotic transients

Robotica ◽

10.1017/s0263574799001952 ◽

2000 ◽

Vol 18 (2) ◽

pp. 201-208 ◽

Cited By ~ 3

Author(s):

V. Paar ◽

N. Pavin ◽

N. Paar ◽

B. Novaković

Keyword(s):

Nonlinear Dynamics ◽

Mathematical Model ◽

Control Parameter ◽

Complex Structure ◽

Degree Of Freedom ◽

Transient Chaos ◽

Regular Pattern ◽

Single Degree ◽

Engineering Significance ◽

Chaotic Transients

In Part 1 of this paper we have investigated numerically the quasiperiodic and frequency locked solutions of mathematical model of a robot with one degree of freedom. In this paper we extend our investigations to the region of transient chaos. The zones of chaotic transients are very broad and lie beyond the parameter range of engineering significance. Transiently chaotic zones exhibit a complex structure, fractally intertwined with tongues of regular pattern and cover a broad range of control parameter L. The crisis point for the onset of sustained chaos lies extremely far from the point of onset of transient chaos.

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Simulation Analysis of One Degree of Freedom Motion of Electromagnetic Spherical Joint based on Maxwell

Journal of Physics Conference Series ◽

10.1088/1742-6596/2085/1/012014 ◽

2021 ◽

Vol 2085 (1) ◽

pp. 012014

Author(s):

Haoran Wang ◽

Fucong Liu ◽

Sai Lou

Keyword(s):

Mathematical Model ◽

Simulation Analysis ◽

Lagrange Equation ◽

Degree Of Freedom ◽

Spherical Joint ◽

Single Degree Of Freedom ◽

Single Degree ◽

Structure And Motion ◽

The Mathematical Model ◽

The Relationship

Abstract In order to improve the stiffness of the spherical joint of the robot, reduce the difficulty of manufacturing and the complexity of the control system, this paper proposed a method of spherical joint and digital drive of the robot based on the electromagnetic principle. Firstly, introduces the structure and motion principle of the spherical joint of the robot, establishes the mathematical model of the spherical joint and establishes the dynamic model according to the second Lagrange equation. after that, the relationship between the number of ampire-turns of the electromagnet on the spherical joint, the attitude Angle of the rotor and the force of the rotor was obtained by simulating the single degree of freedom of the joint based on Ansys maxwell and Matlab, which provided a basis for the realization of the digital drive of the spherical joint.

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