We review the concept of instantaneous center of rotation and its loci, the moving centrode and the fixed centrode, for the plane motion of an arbitrarily shaped rigid body. Then we recall a simple example from the literature. Finally, we present two new solutions pertaining to the motion of an elliptical lamina on a fixed plane, and of a stick moving on an oblique corner.
WilliamsH. E., ‘A note on the use of the instant center as a reference point for angular momentum theorems’, Int. J. Mech. Enging. Educ., 28 (2) (2000), 185–186.
2.
BeerF. P. and JohnstonE. R.Jr, Vector Mechanics for Engineers: Dynamics (McGraw Hill, New York, 1962).
3.
HigdonA.StilesW. B.DaviesA. W. and EvcesC. R., Engineering Mechanics (Prentice Hall, Englewood Cliffs, NJ, 1976).
4.
WillsonF. N., Theoretical and Practical Graphics (Princeton, 1898).
5.
MoonF. C., Franz Reuleaux: Contributions to 19th Century Kinematics and Theory of Machines (preprint, Cornell University, 2002).
6.
This reference is an exception and covers basic kinematics, to the extent that it is useful for machines and mechanisms: Theory of Machines and Mechanisms, UickerJ. J.JrPennockG. R. and ShigleyJ. E. (Oxford University Press, New York, 2003).
LackzikB., ‘Measuring of gears with general (non-circular) pitch curve’, Proc. Inst. Nat. Eng. Soc. (2001), 373.
9.
LitvinF. L., Gear Geometry and Applied Theory (Prentice Hall, New York, 1994).
10.
PearcyM. J. and BogdukN., ‘Instantaneous axes of rotation of the lumbar intervertebral joints’, Spine, 13 (1988), 1033.
11.
BullA. M. J. and MissA. A., ‘Kee joint motion: Description and measurement’, Proc. Instn. Mech. Engrs., 212 (1998), 357.
12.
BreakeyJ. W. and MarquetteS. H., ‘Beyond the four-bar knee’, J. Prosthetics Orthotics, 10 (1998), 77.
13.
ThorntonA. W. and PredeckiP., ‘Design and considerations in a rolamite knee joint prosthesis’, J. Biomed. Materials Res, 7 (2005), 419.
14.
ZwikkerC., The Advanced Geometry of Plane Curves and Their Applications (Dover, New York, 1963).
15.
WalkerR. J., Algebraic Curves (Dover, New York, 1950).
16.
LawrenceJ. D., A Catalog of Special Plane Curves (Dover, New York, 1972).
17.
BloomJ. and WhittL., ‘The geometry of rolling curves’, Am. Math. Month., 88 (1981), 420.
18.
De La HireP., Nouvelle Méthode en Geometrie (Les Planiconiques, Paris, 1673).
19.
De La HireP., Traitè de Mécanique (Paris, 1729).
20.
The Catholic Encyclopedia, vol. 8 (Robert Appleton, New York, 1910).
21.
CeccarelliM., ‘Preliminary studies to screw theories in the 18th century’, Proceedings of Symposium Commemorating the Legacy, Works, and Life of Sir Robert Stawell Ball (Trinity College, University of Cambridge, 9–11 July, 2000).
22.
VarronisM., De Motu Tractatus (Ex Iacobi Stoer, Geneve, 1584).
EulerL., Opera Omnia, Theoria motus corpurum Solidorum seu rigidorum (1760).
25.
BallR. S., A Treatise on the Theory of Screws (Cambridge University Press, Cambridge, 1900).
26.
MeriamJ. L., Dynamics (Wiley, New York, 1966).
27.
WillisR., Principles of Mechanics (London, 1841).
28.
KoetsierT., ‘Mechanisms and machine science: Its history and its identity’, in International Symposium on History of Machines (ed. CeccarelliM.) (Kluwer Academic Publishing, Dordrecht, 2000).
29.
ReuleauxF., Der Constructeur: Ein Handbuch zum Gebrauch beim Maschinen-Entwerfen (Verlag von Friedrich Vieweg und Sohn, Braunschweig, 1861).
30.
KennedyH. C., Life and Works of Giuseppe Peano (Dordrecht, 1980).
31.
ChebyshevP., Ouvres de P.L. Tchebychef. (Chelsea, New York, 1962).
32.
AppellP. and DauthevilleS., Précis de mécanique rationnelle, 2nd ed, ch. 2 (Gauthiers-Villars, Paris, 1918).
33.
OsgoodW. F., Mechanics, ch. 5 (Macmillan, New York, 1937).
34.
AppellP., Traité de Mécanique Rationnelle (Gauthier-Villars, Paris, 1919).
35.
PonceletJ. V., Traité des propiértés projectives des figures (Paris, 1822).
36.
AdamPuig P., Curso de Geometría Métrica, second volume, complements, 9th edn, lecture 29, § 4 (Biblioteca Matemática, Madrid, 1970).
