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Abstract
Air muscle is essentially a robotic actuator which is replacing the conventional pneumatic cylinders at a rapid pace. Due to their low production costs and very high power to weight ratio, as high as 400:1, the preference for Air Muscles is increasing. Air Muscles find huge applications in biorobotics and development of fully functional prosthetic limbs, having superior controlling as well as functional capabilities compared with the current models. This paper discusses Air Muscles in general, their construction, and principle of operation, operational characteristics and applications.
Introduction
Robotic actuators conventionally are pneumatic or hydraulic devices. They have many inherent disadvantages like low operational flexibility, high safety requirements, and high cost operational as well as constructional etc. The search for an actuator which would satisfy all these requirements ended in Air Muscles. They are easy to manufacture, low cost and can be integrated with human operations without any large scale safety requirements. Further more they offer extremely high power to weight ratio of about 400:1. As a comparison electric motors only offer a power ration of 16:1. Air Muscles are also called McKibben actuators named after the researcher who developed it.
History
It was in 1958 that R.H.Gaylord invented a pneumatic actuator which’s original applications included a door opening arrangement and an industrial hoist. Later in 1959 Joseph.L.McKibben developed Air Muscles. The source of inspiration was the human muscle itself, which would swell when a force has to be applied. They were developed for use as an orthotic appliance for polio patients. Clinical trials were realisd in 1960s. These muscles were actually made from pure rubber latex, covered by a double helical weave (braid) which would contract when expanded radially. This could actually be considered as a biorobotic actuator as it operates almost similar to a biological muscle.
The current form air muscles were developed by the Bridgestone Company, famous for its tires. The primary material was rubber i.e. the inner tube was made from rubber. Hence these actuators were called ‘Rubbertuators’. These developments took place around 1980s.
Later in 1990s Shadow Robotic Company of the United Kingdom began developing Air Muscles. These are the most commonly used air muscles now and are associated with almost all humanoid robotic applications which were developed recently. Apart from Shadow another company called The Merlin Humaniform develops air muscles for the same applications, although their design is somewhat different from the Shadow muscles.
Construction
The Air Muscle consists of an inner rubber tube, which is often made from pure rubber latex. It is surrounded by a braided mesh.
The header at each end of the muscle consists of an Aluminium ring, and a
Delrin plastic bung, with a female thread. This thread can be used as a means of attachment, and to allow air into or out of the muscle. The muscle is supplied with two Delrin fittings also.
Working
The inner rubber tube is inflated by entering air at a pressure, usually limited to 3.5 bar. The movement of this tube is constrained by the braid. When the tube gets inflated it experiences a longitudinal contraction. This would create a pull at both ends of the tube. Usually one end of the tube will be attached to somewhere so that force can be applied from one end. This pull when effectively utolised could provide the necessary motion. The working of the Air Muscle closely resembles that of the natural muscle and hence the name Muscle given to it along with Air. The figure below shows the physical appearance of the muscle at different stages of its working.
Theoretical Model
Using conservation of energy and assuming the actuator maintains dV dP equal to zero, reasonable for actuators built with stiff braid fibers that are always in contact with the inner bladder, the tensile force produced can be calculated from:
F¬¬¬¬f describes the lumped effects of friction arising from sources such as contact between the braid and the bladder and between the fibers of the braid itself. Neglecting the second and third terms on the right hand side of above equation and assuming the actuator maintains the form of a right circular cylinder with an infinitesimally thin bladder yields known solutions. The solution to the second term on the right side of the equation is based on a non-linear materials model developed by Mooney and Rivlin in the 1940’s and 1950’s proposed a relationship between stress (σ ) and strain (ε ) given by σ = dW dε where W is the strain
energy density function. Using the assumptions of initial isotropy and incompressibility, W can be described as a function of two strain invariants ( I1 and I2 ):
where Cij are empirical constants. Only two Mooney-Rivlin constants (C10 =118.4 kPa
and C01 =105.7 kPa) were necessary for accurate results with the natural latex rubber bladder, however, other materials may require additional constants. For the case of the McKibben actuator, the experimental methods required to determine these constants are dramatically simplified because the McKibben actuator’s strain invariants, constrained by braid kinematics, are nearly the same as the strain invariants for uniaxial tension .This fortuitous relationship eliminates the need for multi-axial testing that would otherwise be necessary. Solving equation a using the non-linear Mooney-Rivlin materials model results in a McKibben actuator model whose structure is allowed to deform as well as store elastic energy in a non-linear fashion. This model is given by: