{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,2]],"date-time":"2026-05-02T09:58:32Z","timestamp":1777715912669,"version":"3.51.4"},"reference-count":59,"publisher":"SAGE Publications","issue":"1","license":[{"start":{"date-parts":[[2009,9,28]],"date-time":"2009-09-28T00:00:00Z","timestamp":1254096000000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/journals.sagepub.com\/page\/policies\/text-and-data-mining-license"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["The International Journal of Robotics Research"],"published-print":{"date-parts":[[2010,1]]},"abstract":"<jats:p>Quasistatic legged locomotion over uneven terrains requires characterization of the mechanism\u2019s feasible equilibrium postures. This paper characterizes the feasible equilibrium postures of mechanisms supported by three frictional point contacts in a three-dimensional gravitational environment, for a subclass of contact arrangements, calledtame , for which the friction cones lie above the plane spanned by the contacts. The kinematic structure of the mechanism is lumped into a single rigid body \u0392 having the same contacts with the environment and a variable center of mass. The equilibrium postures associated with a given set of contacts become the center-of-mass locations of \u0392 that maintain a feasible equilibrium with respect to gravity. The paper establishes the relations between the feasible equilibrium region and the classical support polygon principle. For tame 3-contact arrangements, the paper identifies and characterizes geometrically three types of boundary curves of the feasible equilibrium region, where two of them are obtained is closed-from, and the third is given implicitly as a solution of a set of nonlinear equations, which can be traced numerically. The three types of boundary curves are then associated with the onset of three different modes of non-static contact motions. Finally, the paper reports on experimental results that verify the theoretical predictions by using a 3-legged prototype.<\/jats:p>","DOI":"10.1177\/0278364909347783","type":"journal-article","created":{"date-parts":[[2009,9,28]],"date-time":"2009-09-28T20:18:30Z","timestamp":1254169110000},"page":"3-22","source":"Crossref","is-referenced-by-count":10,"title":["Analytic Characterization of a Class of Three-contact Frictional Equilibrium Postures in Three-dimensional Gravitational Environments"],"prefix":"10.1177","volume":"29","author":[{"given":"Yizhar","family":"Or","sequence":"first","affiliation":[{"name":"Department of Mechanical Engineering, Technion, Haifa 32000, Israel,"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Elon","family":"Rimon","sequence":"additional","affiliation":[{"name":"Department of Mechanical Engineering, Technion, Haifa 32000, 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