Leg mechanism
A leg mechanism (walking mechanism) is a
An early design for a leg mechanism called the Plantigrade Machine by Pafnuty Chebyshev was shown at the Exposition Universelle (1878). The original engravings for this leg mechanism are available.[2] The design of the leg mechanism for the Ohio State Adaptive Suspension Vehicle (ASV) is presented in the 1988 book Machines that Walk.[3] In 1996, W-B. Shieh presented a design methodology for leg mechanisms.[4]
The artwork of
Design goals
- horizontal speed as constant as possible while touching the ground (support phase)[1][6]
- while the foot is not touching the ground, it should move as fast as possible
- constant torque/force input (or at least no extreme spikes/changes)
- stride height (enough for clearance, not too much to conserve energy)
- the foot has to touch the ground for at least half of the cycle for a two/four leg mechanism[1] or respectively, a third of the cycle for a three/six leg mechanism
- minimized moving mass
- vertical center of mass always inside the base of support[1]
- the speed of each leg or group of legs should be separately controllable for steering[6]
- the leg mechanism should allow forward and backward walking[6]
Another design goal can be, that stride height and length etc. can be controlled by the operator.[6] This can relatively easily be achieved with a hydraulic leg mechanism, but is not practicable with a crank-based leg mechanism.[6]
The optimization has to be done for the whole vehicle – ideally the force/torque variation during a rotation should cancel each other out.[1]
History
Richard Lovell Edgeworth tried in 1770 to construct a machine he called a "Wooden Horse", but was not successful.[7][8]
Patents
Patents for leg mechanism designs range from rotating cranks to four-bar and six-bar linkages.[9] See for example the following patents:
- U.S. Patent No. 469,169 Figure Toy, F. O. Norton (1892).
- U.S. Patent No. 1,146,700, Animated Toy, A. Gund (1915). A leg mechanism formed by an inverted slider-crank.
- U.S. Patent No. 1,363,460, Walking Toy, J. A. Ekelund (1920). A leg mechanism formed by a rotating crank with extensions that contact the ground.
- U.S. Patent No. 1,576,956, Quadruped Walking Mechanism, E. Dunshee (1926). A four-bar leg mechanism that shows the coupler curve forms the foot trajectory.
- U.S. Patent No. 1,803,197, Walking Toy, P. C. Marie (1931). Another rotating crank leg mechanism.
- U.S. Patent No. 1,819,029, Mechanical Toy Horse, J. St. C. King (1931). A crank-rocker leg mechanism with a one-way friction mechanisms in the foot.
- U.S. Patent No. 2,591,469, Animated Mechanical Toy, H. Saito (1952). An inverted slider crank mechanism for the front foot and crank-rocker for the back foot.
- U.S. Patent No. 4095661, Walking Work Vehicle, J. R. Sturges (1978). A lambda mechanismcombined with a parallelogram linkage to form a translating leg that follows the coupler curve.
- U.S. Patent No. 6,260,862, Walking Device, J. C. Klann (2001). The coupler curve of a four-bar linkage guides the lower link of an RR serial chain to form a leg mechanism, known as the Klann linkage.
- U.S. Patent No. 6,481,513, Single Actuator per Leg Robotic Hexapod, M. Buehler et al. (2002). A leg mechanism that consists of a single rotating crank.
- U.S. Patent No. 6,488,560, Walking Apparatus, Y. Nishikawa (2002). Another rotating crank leg mechanism.
Gallery
Stationary
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Eight-bar leg mechanism [10]
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Tokyo Institute of Technology walking chair[11]
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2 DOF pantograph leg mechanism[12]
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2 DOF leg mechanism of the RPRPR type.[13]
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Strandbeest (applied Jansen linkage)
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Ghassaei Linkage[1]
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Tchebyshevs plantigrade machine[14]
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TrotBot Linkage (without heel linkage)[15]
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TrotBot[16] Linkage Speed Variability as Ground Height Changes
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Strider[16] Linkage Speed Variability as Ground Height Changes
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Strider Linkage[17]
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Foot-Paths of Strandbeest, TrotBot, Strider and Klann Linkages
Walking
* | 4 legs | 6 legs |
---|---|---|
Strandbeest | ||
Ghassaei | ||
Klann linkage 1 | ||
Klann linkage 2 | ||
Plantigrade Mechanism | ||
Trotbot[18] | ||
Strider Linkage[17] | Strider Prototype, 4 legs/side |
Complex mechanism
Shown above are only planar mechanisms, but there are also more complex mechanisms:
See also
- Hexapod (robotics)
- Jansen's linkage
- Kinematics
- Kinematic pairs
- Klann linkage
- Chebyshev's Lambda Mechanism
- Linkage (mechanical)
- Machine
- Mecha
- Mobile robot
References
- ^ a b c d e f Ghassaei, Amanda (20 April 2011). The Design and Optimization of a Crank-Based Leg Mechanism (PDF) (Thesis). Pomona College. Archived (PDF) from the original on 29 October 2013. Retrieved 27 July 2016.
- ^ P. L. Tchebyshev. Plantigrade Machine Engraving. stored in the Musée des arts et métiers du Conservatoire national des arts et métiers Paris, France CNAM 10475-0000.
- ISBN 9780262192743.
- ^ W. B. Shieh (1996). Design and Optimization of Planar Leg Mechanisms Featuring Symmetrical Foot-Point Paths (Thesis). PhD Dissertation, The University of Maryland.
- ^ Theo Jansen. Strangdbeest.
- ^ a b c d e Shigley, Joseph E. (September 1960). The Mechanics of Walking Vehicles: A Feasibility Study (PDF) (Report). University of Michigan Department of Mechanical Engineering. Archived from the original (PDF) on 4 March 2016. Retrieved 27 July 2016. Alt URL
- hdl:1993/3922.
- ISBN 0-374-19440-8. Retrieved 27 July 2016.
- ^ J. Michael McCarthy (March 2019). Kinematic Synthesis of Mechanisms: a project based approach. MDA Press.
- ^ Simionescu, P.A.; Tempea, I. (20–24 June 1999). Kinematic and kinetostatic simulation of a leg mechanism (PDF). 10th World Congress on the Theory of Machines and Mechanisms. Oulu, Finland. pp. 572–577. Retrieved 27 July 2016.
- ^ Funabashi, H.; Takeda, Y.; Kawabuchi, I.; Higuchi, M. (20–24 June 1999). Development of a walking chair with a self-attitude-adjusting mechanism for stable walking on uneven terrain. 10th World Congress on the Theory of Machines and Mechanisms. Oulu, Finland. pp. 1164–1169.
- ^ Simionescu, P.A. (21–24 August 2016). MeKin2D: Suite for Planar Mechanism Kinematics (PDF). ASME 2016 Design Engineering Technical Conferences and Computers and Information in Engineering Conference. Charlotte, NC, USA. pp. 1–10. Retrieved 7 January 2017.
- ISBN 978-1-4822-5290-3.
- ^ "Plantigrade machine — Mechanisms by P. L. Tchebyshev".
- ^ Vagle, Wade. "TrotBot Linkage Plans". DIYwalkers.
- ^ a b "Shigley's Study Applied". DIYwalkers.
- ^ a b Vagle, Wade. "Strider Linkage Plans". DIYwalkers.
- ^ "TrotBot".
External links
- Media related to Leg mechanism at Wikimedia Commons