Overconstrained linkages, not satisfying the Kutzbach mobility criterion, are considered. A mathematical technique is presented for the derivation of overconstraint conditions. Although these are essentially geometrical, the model employs algebraic methods normally used for the displacement analysis of spatial linkages. A complete list of all known four-bar overconstrained linkages with lower-pair joints is given.
Get full access to this article
View all access options for this article.
References
1.
• Those references marked with a dot are referred to on page
2.
• BakerJ E, 1975“The Delassus linkages” in Proceedings of the Fourth World Congress on the Theory of Machines and Mechanisms, Newcastle upon Tyne Ed. FawcettJ N, (Institute of Mechanical Engineers, London) pp 45–49
3.
• BakerJ E, 1978a“Overconstrained 5-bars with parallel adjacent joint axes—I, method of analysis”Mechanism and Machine Theory13213–218
4.
• BakerJ E, 1978b“Overconstrained 5-bars with parallel adjacent joint axes—II, the linkages”Mechanism and Machine Theory13219–234
5.
• BakerJ E, 1978c“An overconstrained 5-bar with a plane of quasisymmetry”Mechanism and Machine Theory13467–474
6.
BakerJ E, 1979a“The E-H-H-H-linkage”Mechanism and Machine Theory14361–372
7.
BakerJ E, 1979bTransactions of the American Society of Mechanical Engineers, Journal of Mechanical Design101509–514
8.
• BakerJ EWaldronK J, 1974“The C-H-C-H-linkage”Mechanism and Machine Theory9285–297
9.
BennettG T, 1903“A new mechanism”Engineering76777–778
10.
BennettG T, 1905“The parallel motion of Sarrut and some allied mechanisms”Philosophical Magazine9803–810
11.
BennettG T, 1914“The skew isogram mechanism”Proceedings of the London Mathematical Society (2nd Series)13151–173
12.
• BricardR, 1897“Mémoire sur la théorie de l'octaèdre articulé”Journal de Mathématiques Pures et Appliquées3113–150
13.
• BricardR, 1927Leçons de Cinématique, Volume 2 (Gauthier-Villars, Paris)
14.
• DelassusE, 1900“Sur les systèmes articulés gauches”Annales de l'École Normale, Paris17446–448
15.
• DelassusE, 1902“Sur les systèmes articulés gauches, deuxième partie”Annales de l'École Normale, Paris19119–128
16.
• DelassusE, 1922“Les chaînes fermées et déformables à quatre membres”Bulletin des Sciences Mathématiques46283–304
17.
DimentbergF M, 1950Opredelenie Polozhenii Prostranstvennykh Mekhanizmov (Izdatel'stvo Akademii Nauk SSSR, Moscow)
18.
• DimentbergF MYoslovichI V, 1966“A spatial four-link mechanism having two prismatic pairs”Journal of Mechanisms1291–300
19.
• GoldbergM, 1943“New five-bar and six-bar linkages in three dimensions”Transactions of the American Society of Mechanical Engineers65649–661
20.
• HuntK H, 1967“Prismatic pairs in spatial linkages”Journal of Mechanisms2213–230
21.
KutzbachK, 1929“Mechanische Leitungsverzweigung”Maschinenbau, der Betrieb8710–716
22.
• MyardF E, 1931a“Contribution à la géométrie des systèmes articulés”Bulletin de la Société Mathématique de France59183–210
23.
• MyardF E, 1931b“Sur les chaînes fermées à quatre couples rotoïdes non concourants, déformables au premier degré de liberié. Isogramme torique”Compte Rendus de l'Académie des Sciences, Paris1921194–1196
24.
PamidiP RSoniA HDukkipatiR V, 1971“Existence criteria of an overconstrained R-R-R-P-R five-link spatial mechanism” in Proceedings of the Third World Congress for the Theory of Machines and Mechanisms, Kupari, Yugoslavia, Volume D pp 189–198
25.
PamidiP RSoniA HDukkipatiR V, 1973“Necessary and sufficient existence criteria of overconstrained five-link spatial mechanisms with helical, cylinder, revolute and prism pairs”Transactions of American Society of Mechanical Engineers, Series B. Journal of Engineering for Industry95737–743
26.
RooneyJ, 1978“A comparison of representations of general spatial screw displacement”Environment and Planning B545–88
27.
• SarrutP, 1853“Note sur la transformation des mouvements, rectilignes, alternatifs, en mouvements circulaires; et réciproquement”Compte Rendu de l'Académie des Sciences, Paris361036–1038
28.
SavageM, 1972“Four-link mechanisms with cylindric, revolute and prismatic pairs”Mechanism and Machine Theory7191–210
29.
• SharikovV I, 1961“Teoriya vintov v strukturnom i kinematicheskom analize par i mekhanizmov” in Trudy Instituta Mashinovedeniya, Seminar po Teorii Mashin i Mekhanimov (Izdatelstvo Akademii Nauk SSSR, Moscow) 22 pp 108–136
30.
SoniA H, 1971“Existence criteria of an overconstrained R-P-R-C-R five-link spatial mechanism” in Proceedings of the Third World Congress for the Theory of Machines and Mechanisms, Kupari Yugoslavia, Volume C pp 179–188
31.
• VoineaR PAtanasiuM C, 1962“Théorie géométrique des vis et quelques applications à la théorie des mécanismes”Revue de Mécanique Appliquée, Bucharest7845–860
32.
• WaldronK J, 1967“A family of overconstrained linkages”Journal of Mechanisms2201–211
33.
• WaldronK J, 1968“Hybrid overconstrained linkages”Journal of Mechanisms373–78
34.
• WaldronK J, 1969“Symmetric overconstrained linkages”Transactions of the American Society of Mechanical Engineers, Series B. Journal of Engineering for Industry91158–162
35.
WaldronK J, 1973a“A study of overconstrained linkage geometry by solution of closure equations—part 1, method of study”Mechanism and Machine Theory895–104
36.
WaldronK J, 1973b“A study of overconstrained linkage geometry by solution of closure equations—part II, four-bar linkages with lower pair joints other than screw joints”Mechanism and Machine Theory8233–247