Abstract
In this paper, a double pendulum model is presented with unilateral rigid constraint under harmonic excitation, which leads to be an asymmetric and non-smooth system. By introducing impact recovery matrix, modal analysis, and matrix theory, the analytical expressions of the periodic solutions for unilateral double-collision will be discussed in high-dimensional non-smooth asymmetric system. Firstly, the impact laws are classified in order to detect the existence of periodic solutions of the system. The impact recovery matrix is introduced to transform the impact laws of high-dimensional system into matrix. Furthermore, by use of modal analysis and matrix theory, an invertible transformation is constructed to obtain the parameter conditions for the existence of the impact periodic solution, which simplifies the calculation and can be easily extended to high-dimensional non-smooth system. Hence, the range of physical parameters and the restitution coefficients is calculated theoretically and non-smooth analytic expression of the periodic solution is given, which provides ideas for the study of approximate analytical solutions of high-dimensional non-smooth system. Finally, numerical simulation is carried out to obtain the impact periodic solution of the system with small angle motion.
Highlights
As the most important actuator among all robot mechanisms, the mechanical arm was an important research subject of robot technology [1,2,3]
With the motion refinement of the manipulator and the installation requirements of the external drive, the gap and damping at the link of the manipulator should be considered, as well as the type and installation mode of the external drive, which can be simplified as a collision double pendulum with external simple harmonic excitation
The collision double pendulum with external excitation can explore the dynamic characteristics of the joint of the external wearable manipulator
Summary
As the most important actuator among all robot mechanisms, the mechanical arm was an important research subject of robot technology [1,2,3]. According to the periodic solution, there are many results solutions of analytical single-degree-of-freedom collision systems with unilateral single-impact bilateral single-impact methods. The existence conditions of periodic solutions ofand single-degree-of-freedom were obtained inwith [19,20], whichsingle-impact provided a theoretical analytical method for obtained studyinginperiodic collision systems unilateral and bilateral single-impact were [19,20], solutions of impact systems. Expression was so complex it is difficult to generalize which provided a theoretical analyticalitsmethod for studying periodicthat solutions of impact systems In terms it is extend the expressionengineering. In this paper, by impact matrix and coupling periodic for unilateral double-impact will be discussed in periodic high-dimensional non-smooth the modalsolutions analysis and matrix theory, the analytical expressions of the solutions for unilateral system.
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