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Biomechanics

Key Terms

  • Biomechanics
  • Bio-inspiration
  • Biomimicry
  • Servo
  • Work Loop
  • Limit Cycle
  • Inverted Pendulum
  • Spring Loaded Inverted Pendulum

Comparison of terms

Biomechanics:

Field of study that combines biology and physics to understand how living organisms move and interact with their environment.

Bio-inspiration:

Taking inspiration from nature and using it to solve human problems or create innovative designs and technologies.

Biomimicry:

An attempt to directly copy features and morphologies seen in nature

Muscles

We are talking about skeletal muscle tissue

https://open.oregonstate.education/aandp/chapter/10-2-skeletal-muscle/

Anatomy & Physiology by Lindsay M. Biga, Sierra Dawson, Amy Harwell, Robin Hopkins, Joel Kaufmann, Mike LeMaster, Philip Matern, Katie Morrison-Graham, Devon Quick & Jon Runyeon is licensed under a Creative Commons Attribution-ShareAlike 4.0 International License, except where otherwise noted.

Muscle Architecture

"Biewener, Animal Locomotion"

Muscle Geometry

Biewener, Animal Locomotion

Variable Behavior

A. Biewener and G. B. Gillis, "Dynamics of muscle function during locomotion: accommodating variable conditions.," J. Exp. Biol., vol. 202, no. Pt 23, pp. 3387–3396, 1999.

Passive and Active Behavior

Biewener, Animal Locomotion

Muscles can do Different things

Roberts, T. J., & Azizi, E. (2011). Flexible mechanisms: the diverse roles of biological springs in vertebrate movement. Journal of Experimental Biology, 214(3), 353–361. https://doi.org/10.1242/jeb.038588

Time-based Interactions

Muscles behave differently because of the timing between external forces and muscle behavior

Biewener, Animal Locomotion

Work Loop

Another perspective of the time-based interactions between muscles the world is the "work loop"

  • Work: the energy required to move an object.
  • Walking is often considered a "limit cycle", "a periodic orbit that is a limit set of the dynamical system"
  • A work loop is a way to visualize and understand the work done on an object as it moves through a closed path or loop.

Biewener, Animal Locomotion
https://en.wikipedia.org/wiki/Work_loop
https://underactuated.mit.edu/simple_legs.html

Muscle Stress vs. Strain

Work loops can be seen within specific muscles as well...

M. A. Daley and A. A. Biewener, "Muscle force-length dynamics during level versus incline locomotion: a comparison of in vivo performance of two guinea fowl ankle extensors.," J. Exp. Biol., vol. 206, no. Pt 17, pp. 2941–58, Sep. 2003.

Terrestrial Locomotion

IP vs SLIP

  • "Inverted Pendulum"
  • "Spring-loaded inverted pendulum" *

Passive Dynamic Walkers

Credit: Andy Ruina, Cornell https://www.youtube.com/embed/FfKQSUhYjlY

SLIP Legs

M. H. Raibert, "Legged robots," Artif. Intell. MIT Expand. Front., vol. Vol.2, no. 6, pp. 499–514, 1990.

SLIP's accuracy

Roberts, T. J., & Azizi, E. (2011). Flexible mechanisms: the diverse roles of biological springs in vertebrate movement. Journal of Experimental Biology, 214(3), 353–361. https://doi.org/10.1242/jeb.038588

Implementations of SLIP

A. Sprowitz, A. Tuleu, M. Vespignani, M. Ajallooeian, E. Badri, and A. J. Ijspeert, "Towards dynamic trot gait locomotion: Design, control, and experiments with Cheetah-cub, a compliant quadruped robot," Int. J. Rob. Res., vol. 32, no. 8, pp. 932–950, Jul. 2013.

Leg Stiffness

P. Holmes, R. J. Full, D. Koditschek, and J. Guckenheimer, “The Dynamics of Legged Locomotion: Models, Analyses, and Challenges,” SIAM Rev., vol. 48, no. 2, pp. 207–304, Jan. 2006, doi: 10.1137/S0036144504445133.

Gaits

Biewener, Animal Locomotion

Gait Patterns

Biewener, Animal Locomotion

Walk

A. E. Minetti and L. P. Ardigo, "The Relationship Between Mechanical Work and Energy Expenditure of Locomotion in Horses.," J. Exp. Biol., vol. 202, no. 17, p. 2329, 1999.

Trot

A. E. Minetti and L. P. Ardigo, "The Relationship Between Mechanical Work and Energy Expenditure of Locomotion in Horses.," J. Exp. Biol., vol. 202, no. 17, p. 2329, 1999.

Gallop

A. E. Minetti and L. P. Ardigo, "The Relationship Between Mechanical Work and Energy Expenditure of Locomotion in Horses.," J. Exp. Biol., vol. 202, no. 17, p. 2329, 1999.

Types of Models

Templates and Anchors

Full, R. J., & Koditschek, D. E. (1999). Templates and anchors: neuromechanical hypotheses of legged locomotion on land. Journal of Experimental Biology, 202(23), 3325–3332. https://doi.org/10.1242/jeb.202.23.3325

Example: Cockroach Legs

Full, R. J., & Koditschek, D. E. (1999). Templates and anchors: neuromechanical hypotheses of legged locomotion on land. Journal of Experimental Biology, 202(23), 3325–3332. https://doi.org/10.1242/jeb.202.23.3325

Metrics & Scaling Laws

Speed vs. Metabolic Cost

A. E. Minetti and L. P. Ardigo, "The Relationship Between Mechanical Work and Energy Expenditure of Locomotion in Horses.," J. Exp. Biol., vol. 202, no. 17, p. 2329, 1999.

Cost of Transport

\(COT = \frac{P}{mgv}\) (J/m/kg)

  • the smaller the COT the more energy-effective
  • different COTs depending on what "powers" are included (total, locomotion, mechanical, etc)
  • sometimes referred to as specific resistance

COT in Animals

Tucker, V. A. “The Energetic Cost of Moving About: Walking and Running Are Extremely Inefficient Forms of Locomotion. Much Greater Efficiency Is Achieved by Birds, Fish—and Bicyclists.” American Scientist, vol. 63, no. 4, Sigma Xi, The Scientific Research Society, 1975, pp. 413–19, http://www.jstor.org/stable/27845576.

COT in Robots

Baisch, A. T., Ozcan, O., Goldberg, B., Ithier, D., & Wood, R. J. (2014). High speed locomotion for a quadrupedal microrobot. The International Journal of Robotics Research. https://doi.org/10.1177/0278364914521473

COT in both

S. Seok et al., “Design Principles for Energy-Efficient Legged Locomotion and Implementation on the MIT Cheetah Robot,” IEEE/ASME Trans. Mechatron., vol. 20, no. 3, pp. 1117–1129, Jun. 2015, doi: 10.1109/TMECH.2014.2339013.

Froude Number

\[Fr = v^2/gl\]
  • Essentially the ratio of kinetic to potential energy
  • often viewed as a dimensionless number
  • l is a characteristic leg length (often taken in running robots as the distance from the hip to the ground)
  • dynamically similar legged locomotors should exhibit equal ratios of inertial to gravitation forces for equivalent gaits

Similar across

Alexander, R. M. & Jayes, A. S. A dynamic similarity hypothesis for the gaits of quadrupedal mammals. J. Zool. 135–152 (1983). doi:10.1111/j.1469-7998.1983.tb04266.x

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