Dynamic analysis of microrobots with Coulomb friction using harmonic balance method

Abstract

In this paper, we investigate the dynamic analysis of a strongly nonlinear microrobot using a three-term harmonic balance method. The employed locomotion concept, namely "friction drive principle," is based on the superposition of a horizontal vibration at the interface between the robot and work floor and an active variation of friction force, obtained by the vertical vibration of the base at the same interface. The equation of motion for the system reveals a parametrically excited oscillator with discontinuity for which the elastic force term is proportional to a signum function. The obtained periodic solution not only is of high accuracy, but also can predict the contribution of the friction coefficient in the average velocity of the slider. Results show that the velocity and the step efficiency of motion depend almost sinusoidally on the phase shift between the horizontal and the vertical vibration. Unlike traditional analytical techniques and in agreement with both numerical simulations and experimental results reported in the literature, the utilized method demonstrates that the maximum average velocity occurs at a phase shift that varies with respect to system's configuration parameters. Besides, the effect of variation of different configuration parameters on the behavior of this type of microrobots has been studied and the maximum achievable performance in terms of velocity and the step efficiency has been evaluated.

Optimized adaptive tracking control for an underactuated vibro-driven capsule system

“…Based on the optimized trajectory model studied in Sect. 3, the parameters for the constructed trajectory (9) and the trajectory in [20] are detailed in Table 1. The simulation results are presented in Figs.…”

“…Motion principle of the microrobotic systems is one of the crucial issues that determine the capabilities, performance, particularly energy consumption and degrees of autonomy. Some motion systems have been designed and utilized via mimicking the worm progression [6,7], canoe paddling [8], friction drive [9] and magnetic field [10,11], which feature complex mechanism structures and make the issue of motion control a challenging task. The vibro-impact capsule systems (e.g.…”

Chaos study of a vibratory micro-robot in hybrid motion

“…(6), (7), and (10), we observe that the motion of micro-robot is related to α, μ 0 /μ, ϕ, β and e. According to Eqs. (5) and (8), we obtain that the horizontal velocity of micro-robot is directly proportional to the friction coefficient and inversely related to the frequency of stimulation (applied forces). It should be noted that some effective parameters in the movement of micro-robot are functions of the friction coefficient and the frequency of excitation.…”

“…Motion mechanisms of the most micro-robots are based on the friction drive principle that leads to stick-slip motion [4,5]. This principle has two parts: the slip generation and the slip variation [2,3].…”

Wavelet basis expansion-based spatio-temporal Volterra kernels identification for nonlinear distributed parameter systems

“…It is well known that nonlinear system can be generally divided into nonlinear lumped parameter systems and nonlinear distributed parameter systems (DPS). To understand those dynamic behaviors of nonlinear lumped parameter systems, various theories and methods have been developed, such as chaos [2,3], nonlinear time series analysis methods [4][5][6], the multiple scales method [7,8], the KBM method, and harmonic balance method [9]. Unfortunately, modeling the nonlinear DPS which are described in terms of nonlinear partial differential equations (PDEs) is a challenging task because of the infinite-dimensional and nonlinear properties.…”