Pennate actuators: force, contraction and stiffness

Hierarchical actuators are comprised of multiple individual actuator elements arranged into a system, resulting in improved and expanded performance. Natural muscle tissue is a complex and multi-level example of hierarchical actuation, with its hierarchy spanning from the micrometer to the centimeter scale. In addition to a hierarchical configuration, muscle tissue exists in varying geometric arrangements. Pennate muscle tissue, denoted by its characteristic fibers extending obliquely away from the muscle tissue line of action, leverages geometric complexity to transform the relationship between fiber inputs and muscle tissue outputs. In this paper, a bioinspired hierarchical pennate actuator is detailed. This work expands on previous pennate actuator studies by deriving constitutive force, contraction, and stiffness models for a general pennate actuator, where the constituent fibers can be constructed from any linear actuator. These models are experimentally validated by studying a pennate actuator with McKibben artificial muscles constituting the actuator fibers. McKibben artificial muscles are used because they have a high force-to-weight ratio and are inexpensive to construct, making them an attractive candidate for hierarchical actuators and mobile robotics. Using the derived constitutive models, general pennate actuator performance is better understood by analyzing the transmission ratio, blocked force, and free contraction. Loaded contractions and stiffness during isotonic and isobaric contractions are also explored. The results allow for informed design decisions and an understanding of the associated tradeoffs when recreating the remarkable properties of pennate musculature. Future work will leverage the results of this paper to create an adaptive pennate actuator that is capable of changing configuration in response to force, contraction and stiffness demands.