Leg mechanism

• horizontal speed as constant as possible while touching the ground (support phase){{cite report |author=Shigley, Joseph E. |title=The Mechanics of Walking Vehicles: A Feasibility Study |publisher=University of Michigan Department of Mechanical Engineering |date=September 1960 |url=http://www.dtic.mil/dtic/tr/fulltext/u2/419858.pdf |archiveurl=https://web.archive.org/web/20160304045205/http://www.dtic.mil/dtic/tr/fulltext/u2/419858.pdf |archivedate=4 March 2016 |url-status=dead |accessdate=27 July 2016}} [http://hdl.handle.net/2027.42/7574 Alt URL]
• 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 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
• the speed of each leg or group of legs should be separately controllable for steering
• the leg mechanism should allow forward and backward walking

Another design goal can be, that stride height and length etc. can be controlled by the operator. This can relatively easily be achieved with a hydraulic leg mechanism, but is not practicable with a crank-based leg mechanism.

The optimization has to be done for the whole vehicle – ideally the force/torque variation during a rotation should cancel each other out.

Richard Lovell Edgeworth tried in 1770 to construct a machine he called a "Wooden Horse", but was not successful.{{cite thesis |title=Design and optimization of a one-degree-of-freedom eight-bar leg mechanism for a walking machine |author=Giesbrecht, Daniel |date=8 April 2010 |publisher=University of Manitoba |hdl = 1993/3922}}{{cite book |url=https://archive.org/details/lunarmenfivefrie00uglo |title=The Lunar Men: Five Friends Whose Curiosity Changed the World |author=Uglow, Jenny |publisher=Farrar, Straus and Giroux |date=2002 |location=New York, New York |isbn=0-374-19440-8 |accessdate=27 July 2016 |url-access=registration }}

Patents for leg mechanism designs range from rotating cranks to four-bar and six-bar linkages.{{cite book|author=J. Michael McCarthy|title=Kinematic Synthesis of Mechanisms: a project based approach|publisher=MDA Press|date=March 2019|url=https://mechanicaldesign101.com/2019/03/25/kinematic-synthesis-of-mechanisms-a-project-based-approach/}} See for example the following patents:

• [https://patents.google.com/patent/US469169A/en?oq=U.S.+Patent+No.+469%2c169+Figure+Toy U.S. Patent No. 469,169 Figure Toy, F. O. Norton (1892)].
• [https://patents.google.com/patent/US1146700A/en?oq=U.S.+Patent+No.+1%2c146%2c700%2c+Animated+Toy U.S. Patent No. 1,146,700, Animated Toy, A. Gund (1915)]. A leg mechanism formed by an inverted slider-crank.
• [https://patents.google.com/patent/US1363460A/en?oq=U.S.+Patent+No.+1%2c363%2c460%2c+Walking+Toy 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.
• [https://patents.google.com/patent/US1576956A/en?oq=U.S.+Patent+No.+1%2c576%2c956%2c+Quadruped+Walking+Mechanism 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.
• [https://patents.google.com/patent/US1803197A/en?oq=U.S.+Patent+No.+1%2c803%2c197%2c+Walking+Toy U.S. Patent No. 1,803,197, Walking Toy, P. C. Marie (1931)]. Another rotating crank leg mechanism.
• [https://patents.google.com/patent/US1819029A/en?oq=U.S.+Patent+No.+1%2c819%2c029%2c+Mechanical+Toy+Horse 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.
• [https://patents.google.com/patent/US2591469A/en?oq=U.S.+Patent+No.+2%2c591%2c469%2c+Animated+Mechanical+Toy 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.
• [https://patents.google.com/patent/US4095661A/en?oq=U.S.+Patent+No.+4095661%2c+Walking+Work+Vehicle U.S. Patent No. 4095661, Walking Work Vehicle, J. R. Sturges (1978)]. A lambda mechanism combined with a parallelogram linkage to form a translating leg that follows the coupler curve.
• [https://patents.google.com/patent/US6260862B1/en?oq=U.S.+Patent+No.+6%2c260%2c862%2c+Walking+Device 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.
• [https://patents.google.com/patent/US6481513B2/en?oq=U.S.+Patent+No.+6%2c481%2c513%2c+Single+Actuator+per+Leg+Robotic+Hexapod 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.
• [https://patents.google.com/patent/US6488560B2/en?oq=U.S.+Patent+No.+6%2c488%2c560%2c+Walking+Apparatus U.S. Patent No. 6,488,560, Walking Apparatus, Y. Nishikawa (2002)]. Another rotating crank leg mechanism.

File:Strandbeest-Walking-Animation.gif|Jansen linkage

File:F4-motion.gif|Klann linkage

File:Leg mechanism.gif|Eight-bar leg mechanism {{cite conference |author1=Simionescu, P.A. |author2=Tempea, I. |title=Kinematic and kinetostatic simulation of a leg mechanism |conference=10th World Congress on the Theory of Machines and Mechanisms |location=Oulu, Finland |date=20–24 June 1999 |pages=572–577 |url=http://faculty.tamucc.edu/psimionescu/PDFs/Simionescu-IFToMM-1999.pdf |accessdate=27 July 2016 }}

File:Tokyo Institute of Technology leg mechanism.gif|Tokyo Institute of Technology walking chair{{cite conference |author1=Funabashi, H. |author2=Takeda, Y. |author3=Kawabuchi, I. |author4=Higuchi, M. |title=Development of a walking chair with a self-attitude-adjusting mechanism for stable walking on uneven terrain |conference=10th World Congress on the Theory of Machines and Mechanisms |location=Oulu, Finland |date=20–24 June 1999 |pages=1164–1169 }}

File:Strandbeest--Full-Walking-Animation.gif|Strandbeest (applied Jansen linkage)

File:Ghassaei Linkage four legs.gif|Ghassaei Linkage

File:Tchebyshevs plantigrade machine.gif|Tchebyshevs plantigrade machine{{Cite web | url=http://en.tcheb.ru/1 | title=Plantigrade machine — Mechanisms by P. L. Tchebyshev }}

File:TrotBot without Heel Linkage.gif|TrotBot Linkage (without heel linkage){{cite web |last1=Vagle |first1=Wade |title=TrotBot Linkage Plans |url=https://www.diywalkers.com/trotbot-linkage-plans.html |website=DIYwalkers}}

File:TrotBot - 1 Corner of 12 Leg Robot.gif|TrotBot{{cite web |title=Shigley's Study Applied |url=https://www.diywalkers.com/blog/walking-tanks-prof-shigleys-pioneering-study-of-mechanical-walkers |website=DIYwalkers}} Linkage Speed Variability as Ground Height Changes

File:Strider Linkage - 1 Corner of 12 Leg Robot.gif|Strider Linkage Speed Variability as Ground Height Changes

File:Strider Linkage Animated.gif|Strider Linkage{{cite web |last1=Vagle |first1=Wade |title=Strider Linkage Plans |url=https://www.diywalkers.com/strider-linkage-plans.html |website=DIYwalkers}}

File:Strandbeest, TrotBot, Strider, Klann Linkages.gif|Foot-Paths of Strandbeest, TrotBot, Strider and Klann Linkages

Shown above are only planar mechanisms, but there are also more complex mechanisms:

File:Lauron4c 2009 FZI Karlsruhe.jpg

File:Legged robot.jpg

File:Sechsbeiniger Laufroboter LAURON aus dem Jahr 1995 im Deutschen Museum in München entwickelt vom Forschungszentrum Informatik, Karlsruhe.jpg

• Hexapod (robotics)
• Jansen's linkage
• Kinematics
• Kinematic pairs
• Klann linkage
• Chebyshev's Lambda Mechanism
• Linkage (mechanical)
• Machine
• Mecha
• Mobile robot

{{reflist|30em}}

{{Wikibooks|Comparison of crank based leg mechanism}}

{{Use dmy dates|date=March 2018}}

• {{Commonscatinline}}

Category:Linkages (mechanical)