Christopher George Gibson
Email: gibson@sms.edu.pk
Course: Geometry
Publications
01. Gibson,C.G. The Radon Integral in Intuitionism.
Thesis. University of Amsterdam. V.R.B. Groningen. (1967).
02. Gibson,C,G. The Intuitionist Measure. J. London Math. Soc., 44 (1969) 617-624.
03. Gibson,C.G. On the Definition of an Infinite Species. Nieuw Archief voor
Wiskunde XIX. (1971) 196-197.
04. Gibson,C.G. On the Almost Periodicity of Trigonometric Polynomials in Constructive
Mathematics. Indag. Maths. 34 (1972) 355-361.
05. Gibson,C.G. Construction of Canonical Stratifications. In: Topological Stability
of Smooth Mappings. Lecture Notes in Mathematics, 552, Springer Verlag, Berlin
(1976) 9-34.
06. Gibson,C.G. Regularity of the Segre Stratification. Math. Proc. Camb. Phil.
Soc. 82 (1977) 91-97.
07. Bedford,J.O. and Gibson,C.G. On Stratifying 3-Jets of Functions.it Math.
Proc. Phil. Camb. Soc. 82 (1977) 389-400.
08. Bedford,J.O. and Gibson,C.G. Regularity Conditions over the First Simple
Elliptic Family. J. London Math. Soc. (2), 20 (1979) 343-346.
09. Gibson,C.G. Singular Points of Smooth Mappings. Research Notes in Mathematics.
Pitman, London, (1979) 239pp.
10. Bedford,J.O. and Gibson,C.G. Regularity Conditions over the Second Simple
Elliptic Family. J. London Math. Soc. (2) 21 (1980) 371-378.
11. Bruce,J.W., Giblin,P.J. and Gibson,C.G. Sur les Caustiques par Reflexion.
C.R. Acad. Sc. Paris 290 A (1980) 325-326.
12. Bruce,J.W., Giblin,P.J. and Gibson,C.G. On Caustics of Plane Curves. American
Mathematical Monthly. (88) 9 (1981) 651-667.
13. Giblin,P.J. and Gibson,C.G. On Regularity Conditions over Exceptional Unimodular
Families of Singularities. Quarterly J. of Maths. Oxford (2) 32 (1981) 23-43.
14. Johns,D.L. and Gibson, C.G. A Constructive Approach to the Duality Theorem
for Certain Orlicz Spaces. Math. Proc. Camb. Phil. Soc. 89 (1981) 49-69.
15. Bruce,J.W., Giblin,P.J. and Gibson,C.G. On Caustics by Reflexion. Topology.
(21) 2 (1982) 179-199.
16. Bruce,J.W., Giblin,P.J. and Gibson,C.G. Source Genericity for Caustics by
Reflexion in the Plane. Quarterly J. of Math. Oxford (2) 33 (1982) 169-190.
17. Bruce,J.W., Giblin,P.J. and Gibson,C.G. Source Genericity for Caustics by
Reflexion in R3. Proceedings of the Royal Society. London. A 381 (1982) 83-116.
18. Gibson,C.G., and Ward,T.J. On Stratifying Pairs of Linear Mappings. Pacific
J. of Maths. (102) 2 (1982) 1-17.
19. Dimca,A. and Gibson,C.G. On the Unfolding of the First Contact Unimodular
Family for Germs of the Plane. Quart. J. Math. Oxford. 920 (1982) 1-8.
20. Dimca,A and Gibson,C.G. Contact Unimodular Germs from the Plane to the Plane.
Quart. J. Math.Oxford 2 (1982) 1-15.
21. Gibson,C.G. Review of `Cusps of Gauss Mappings' by T.Banchoff, T.Gaffney
and C.McRory in Mathematical Intelligencer 5, No 2 (1982) 51-52.
22. Bruce,J.W., Giblin,P.J. and Gibson,C.G. Caustics by Reflexion in the Extended
Plane. Geometria Dedicata. 15 (1983) 171-194.
23. Bruce,J.W., Giblin,P.J. and Gibson,C.G. Genericity of Caustics by Reflexion.
AMS Proceedings of Symposia in Mathematics. Vol. 40 (Singularities) Part 1 (1983)
179-193.
24. Dimca,A. and Gibson,C.G. Contact Germs from the Plane to the Plane. AMS
Proceedings of Symposia in Pure Mathematics. Vol.40 (Singularities) Part 1 (1983)
277-282.
25. Gibson,C.G. Review of `Singularities of Smooth Functions and Differentiable
Maps' by J.Martinet in Bull. London Math. Soc., 15 (1983) 173-174.
26. Gibson,C.G. Review of `Introduction to Differential Topology' by T.Brocker
and K.Janich in the Times Higher Education Supplement. (1983)
27. Bruce, J.W., Giblin,P.J. and Gibson,C.G. Caustics Through the Looking Glass.
Mathematical Intelligencer. (1984) 47-58.
28. Bruce,J.W., Giblin,PJ. and Gibson,C.G. Caustics in Extended Euclidean Space.
SIAM J. Math. Anal. 15 (1984) 50-68.
29. Bruce,J.W. and Gibson,C.G. Distance Genericity for Real Algebraic Hypersurfaces.
Can. J. Math. Vol. XXXVI 2 (1984) 374-384.
30. Dimca,A. and Gibson,C.G. Classification of Equidimensional Contact Unimodular
Germs. Mathematica Scandinavica 56 (1985) 15-28.
31. Bruce,J.W., Giblin,P.J. and Gibson,C.G. Symmetry Sets. Proc.Royal Soc. Edinburgh.
101A (1985) 163-186.
32. Gibson,C.G. and Newstead,P.E. On the Geometry of the Planar 4-Bar
Mechanism. Acta Applicandae Mathematicae 7 (1986) 113-135.
33. Gibson,C.G. Configuration Spaces in Mechanism and Machine Theory.In: The
Theory of Machines and Mechanisms. Proceedings of the 7th World Congress (1987)
Sevilla, Spain. 267-269.
34. Gibson,C.G. and Selig,J.M. On Movable Hinged Spherical Quadrilaterals. Part
I. The Configuration Space. Mechanism and Machine Theory Vol. 23, No 1, (1988)
13-18.
35. Gibson,C.G. and Selig,J.M. On Movable Hinged Spherical Quadrilaterals. Part
II. Singularities and Reductions. Mechanism and Machine Theory
Vol. 23, No 1, (1988) 19-24.
36. Gibson,C.G. and Marsh,D. Concerning Cranks and Rockers. Mechanism and Machine
Theory. Vol 23, No 5, (1988) 355-360.
37. Gibson,C.G. and Marsh,D. On the Linkage Varieties of the Watt 6-Bar Mechanisms-I:
Basic Geometry. Mechanism and Machine Theory. Vol 24, No 2, (1989) 106-113.
38. Gibson,C.G. and Marsh,D. On the Linkage Varieties of the Watt 6-Bar Mechanisms-II:
The Possible Reductions. Mechanism and Machine Theory. Vol 24, No 2, (1989)
115-121.
39. Gibson,C.G. and Marsh,D. On the Linkage Varieties of the Watt 6-Bar Mechanisms-III:
Topology of the Real Varieties. Mechanism and Machine Theory.
Vol 24, No 2, (1989) 123-126.
40. Gibson,C.G. and Hunt,K.H. Geometry of Screw Systems. Part I. Screws- Genesis
and Geometry. Mechanism and Machine Theory. Vol. 25, No.1, (1990) 1-10.
41. Gibson,C.G. and Hunt,K.H. Geometry of Screw Systems. Part II. Classification
of Screw Systems. it Mechanism and Machine Theory.Vol. 25, No.1, (1990) 11-27.
42. Gibson,C.G. and Marsh,D. On the Geometry of Geared 5-Bar Motion. Journal
of Mechanical Design. Vol. 112, 4, (1990) 620-627.
43. Donelan,P.S. and Gibson,C.G. First Order Invariants of Euclidean Motions.
Acta Applicandae Mathematicae Vol. 24 (1991) 233-251.
44. McAree,P.R., Gibson,C.G., Samuel,A.E. and Hunt,K.H. A Dexterity Measure
for the Kinematic Control of Multi-finger Multi-freedom Robot Hands. International
Journal of Robotics Research Vol. 10, No.5 (1991) 439-453.
45. Gibson,C.G. Review of `Real Algebraic and Semi-Algebraic Sets' by R.Benedetti
and J.J.Risler in Bull. London Math. Soc., 23 (1991) 309-311.
46. Gibson,C.G. Kinematic Singularities - A New Mathematical Tool, Third International
Workshop on Advances in Robot Kinematics, Ferrara, Italy, September (1992) 209-215.
47. Gibson,C.G. and Hobbs,C.A. Simple Singularities of Space Curves. Math. Proc.
Camb. Phil. Soc. 113 (1993) 297-310.
48. Donelan,P.S. and Gibson,C.G. On the Hierarchy of Screw Systems. Acta Applicandae
Mathematicae. 32 (1993) 267-296.
49. Gibson,C.G. Steiner Networks. Mathematics Review. Vol.3, No.4 (1993) 22-25.
50. Gibson,C.G., Hawes, W.H. and Hobbs,C.A. Local Pictures for General Two-Parameter
Motions of the Plane. In `Advances in Robot Kinematics and Computational Geometry',
Kluwer Academic Publishers (1994) 49-58.
51. Gibson,C.G. and Hobbs,C.A. Local Models for General One-Parameter Motions
of the Plane and Space. Proceedings of the Royal Society of Edinburgh, 125A,
(1995) 639-656.
52. Gibson,C.G. and Hawes,W. Bifurcation of General Planar Motions with Three
Degrees of Freedom. In `26th International Symposium on Industrial Robots, Singapore,
1995'. MEP, (1995) 357-361.
53. Gibson,C.G., Marsh,D. and Xiang,Y. An Algorithm to Generate the Transition
Curve of the Planar Four-bar Mechanism. Mechanism and Machine Theory. Vol 31,
No.4 (1996) 381-395.
54. Gibson,C.G. and Hobbs,C.A. Singularity and Bifurcation for General
Two-Dimensional Planar Motions. New Zealand Journal of Mathematics. 25 (1996)
141-163.
55. Donelan,P.S. and Gibson,C.G. Sao Paulo Lectures on Singular Phenomena in
Kinematics. Delivered by the second author as a series of four Main Invited
Lectures at the IV International Workshop on Real and Complex Singularities,
Instituto de Ciencias Matematicas de Sao Carlos, Universidade de Sao Paulo,
Brazil.
56. Gibson,C.G., Marsh,D. and Xiang,Y. A New Philosophy for the Kinematic Design
of Mechanisms. Journal of TPTY, Special issue for the Proceedings of the International
CAD/CAM Conference in Gelengick, Russia. 3 (1997) 28-31.
57. Gibson,C.G., Hobbs,C.A. and Marar,W.L. On Versal Unfoldings of Singularities
for General Two-Dimensional Spatial Motions. Acta Applicandae Mathematicae,
47 (2) (1997) 221-242.
58. Gibson,C.G., Marsh,D. and Xiang,Y. Singular Aspects of Generic Planar Motions
with Two Degrees of Freedom. International Journal of Robotics Research. 17(10)
(1998) 1068-1080.
59. Gibson,C.G. Elementary Geometry of Algebraic Curves. 250 pages. Cambridge
University Press. (1998).
60. Donelan,P.S. and Gibson,C.G. Singular Phenomena in Kinematics. In Singularity
Theory, Edited by Bill Bruce and David Mond, Cambridge University Press.
379-402 (1999).
61. Donelan,P.S., Gibson,C.G. and Hawes,W. Trajectory Singularities of General
Planar Motions. Proceedings of the Royal Society of Edinburgh, 29A, (1999) 37-55.
62. Cocke,M.W., Donelan,P.S. and Gibson,C.G. Instantaneous singular sets associated
to spatial motions. In Real and complex singularities (Sao Carlos, 1998), 147-163,
Chapman and Hall/CRC Res. Notes Math., 412, Edited by F.Tari and J.W.Bruce.
Chapman and Hall/CRC, Boca Raton, FL, 2000. (1999).
63. Gibson,C.G. Kinematics from the Singular Viewpoint. In Geometrical Foundations
of Robotics, 61-78, World Scientific. Edited by J.M.Selig. (2000)
64. Cocke,M.W., Donelan,P.S. and Gibson,C.G. Screw Systems, Singular Trajectories
and Darboux-Type Motions. Submitted to the International Journal of Robotics
Research (2000).
65. Gibson,C.G. Elementary Geometry of Differentiable Curves. 250 pages. Cambridge
University Press. (2001).
66. Cocke,M.W., Donelan,P.S. and Gibson,C.G. A Genericity Lemma for Euclidean
Motions of Darboux Type. In preparation
67. Cocke,M.W., Donelan,P.S. and Gibson,C.G. Genericity of the Planar Four Bar.
In preparation
68. Gibson,C.G. Elementary Euclidean Geometry. 174 pages. Cambridge University
Press. (2004).