Abstract
Recently, the hyperbolic Hill-type force-velocity relation was derived from basic physical components. It was shown that a contractile element CE consisting of a mechanical energy source (active element AE), a parallel damper element (PDE), and a serial element (SE) exhibits operating points with hyperbolic force-velocity dependency. In this paper, a technical proof of this concept was presented. AE and PDE were implemented as electric motors, SE as a mechanical spring. The force-velocity relation of this artificial CE was determined in quick release experiments. The CE exhibited hyperbolic force-velocity dependency. This proof of concept can be seen as a well-founded starting point for the development of Hill-type artificial muscles.
Highlights
Human and animal movement is driven by muscle, a biological elastic actuator
It consisted of three elements: active element AE, parallel damping element parallel damper element (PDE) and serial element SE making up together the contractile element
CE of a Hill-type muscle. y0 represented the origin of the muscle, y1 was the coordinate specifying the length of the AE and the PDE lAE = lPDE = y1 − y0 and y2 the length of the whole contractile element lCE = y2 − y0
Summary
A glance at the complexity and variety of the generated movements shows that muscle is a versatile, powerful, and flexible actuator. This is achieved because muscle can operate in different modes depending on the contraction dynamics and the structural implementation. To interpret the results Hill [12] proposed a macroscopic mathematical model for a contractile element (CE) This CE describes phenomenologically the force-length and the force-velocity dependency of muscle fibers. For the force-velocity relation in concentric contractions (shortening muscle) he found that the muscle fiber shortening velocity depends on the CE force in a hyperbolic relation This hyperbolic relation is known as the Hill relation. Various extensions account for physiologically observable effects, such as contraction history effects [15, 19], high frequency oscillation damping [9], and eccentric contractions [22]
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