A review on nonlinear modes in conservative mechanical systems

Efficient and Goal-Directed Oscillations in Articulated Soft Robots: The Point-To-Point Case

“…produces the unit vectors v 1 , v 2 , ..., v n such that Span{(v j , 0), (0, v j )} is a (twodimensional) eigenspace of (2). Please refer to [16] and references within for more information on modal analysis.…”

“…This is necessary to keep the theory tractable. Consider for example that nonlinear modes for robotic systems are defined only for conservative systems [16]. We will focus on the nonlinear case in future work.…”

“…used to this end [10]- [12], with promising results that however are often limited to particular examples. More recently, a series of works by some of the co-authors [13]- [16] have proven that linear and nonlinear modal theory can be used to guide the excitation of hyper-efficient oscillations in generic soft robots. Yet, these performances are obtained at the cost of accepting whatever oscillatory behavior the system can achieve -regardless of the task's goal.…”

Determining the regions of stability in the motion regimes and parameters of vibratory machines for different technological purposes

“…This approach must additionally clarify the transition from the initial control equations of movements to the equations describing only a slower component of the movements. Article [11] outlines the theory of oscillatory modes and its applicability to general mechanical systems by employing the generalization of modal analysis to a nonlinear case. The article does not define the nature of dissipative forces and their impact on oscillations.…”

“…j is the initial phase of the forcing. By dividing equations (9) and (10) by m, after the transform, we obtain: in the last expressions, and hereafter, the strokes indicate the differentiation for τ).By substituting the resulting expressions in(11) and (12), we obtain the following equations:…”