Mass-spring-damper

A mass-spring-damper system refers to a mechanical system that consists of a mass, a spring, and a damper. The mass represents the object being moved, the spring represents the force that opposes the motion of the mass, and the damper represents the force that dissipates the energy of the system. Together, these components work to create a system that can oscillate or vibrate in response to external forces.From: Modeling and Control of Engineering Systems [2019], Spontaneous gait transition to high-speed galloping by reconciliation between body support and propulsion [2018]

Single Degree‐of‐Freedom Damped Vibration

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Published in Haym Benaroya, Mark Nagurka, Seon Han, Mechanical Vibration, 2017

Haym Benaroya, Mark Nagurka, Seon Han

with the second term, tA2exp(-ωnt) $ tA_{2} {\text{exp }}( - \omega_{n} t) $ , needed to ensure independent solutions. This term is initially driven by t, i.e., the effect of t in som response dominates. later time the exponential decay governs the behavior. From the expressionζ = c/2mωn for a mass‐spring‐damper system, for ζ = 1, the viscous damping coefficient assumes its critical value, ccr=2mωn=2km $ c_{cr} = 2m\omega_{n} = 2\sqrt {km} $ . Equivalently, ζ = c/ccr.

Spontaneous gait transition to high-speed galloping by reconciliation between body support and propulsion

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Published in Advanced Robotics, 2018

A. Fukuhara, D. Owaki, T. Kano, R. Kobayashi, A. Ishiguro

Figure 1 shows the mechanical system of a quadruped robot, simplified as a 2D mass–spring–damper system. The details of interaction between point masses are presented in Appendix A.1. The robot consists of a trunk with four simple limbs, and a point mass is employed at each joint. The limb has two DOF: a rotary actuator at the shoulder/hip joint and a prismatic actuator at the elbow/knee joint. The elbow and knee joints fundamentally cannot bend, and the limb is adjusted via a stiff torsional spring and damper. Additionally, a stiff torsional spring keeps the trunk rigid.

Mass-spring-damper

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Single Degree‐of‐Freedom Damped Vibration

Spontaneous gait transition to high-speed galloping by reconciliation between body support and propulsion