Line and screw systems, used in robotics and machinery analysis, become singular at particular geometric configurations. When not singular, measures are required that describe how far they are from being so. A new system of measures is proposed whose outcome is strictly invariant with respect to coordinate frame, origin and unit of length. Examples of the application of the new measures to sixfold systems of lines and screws in the context of work-holding systems and robotic manipulators are given.
OlmsteadM. A.AmerN. M.HohnS.Rhotothermal displacement spectroscopy: An optical probe for solids and surfaces. Appl. Phys., A,198332, 141–54.
2.
ZimmermanP.WelschE.Modeling of signal detection by using the photothermalprobe beam detection technique. Rev. Sci. Instrum.,1994, 65, 97–101.
3.
YilbasB. S.Optical method for measurement of the temporal variation of temperature at the surface of a metal heated by a laser. J. Optics,1986, 15, 108–116.
4.
WangH. G.GuanY. H.ChenT. L.ZhangJ. T.A study of thermal stresses during laser quenching. J. Mater. Proc. Technol., 1997, 63, 550–553.
5.
GuanY. H.ChenT. L.WangH. G.FangG.The thermal stresses and residual stresses during laser phase transformation process. In Proceeding of Thermal Stresses 1995, Japan, 5 June 1995, pp. 533–536.
6.
LiK.ShengP.Plane stress model for fracture of ceramics during laser cutting. Int. J. Mach. Tools Mfg, 1995, 35, 1493–1506.
7.
YilbasB. S.SamiM.ShujaS. Z.Laser-induced thermal stresses on steel surface. Optics and Lasers in Engng, 1998, 30, 25–37.
8.
YilbasB. S.SbujaS. Z.Laser heating of silicon: A kinetic theory approach. Int. J. Comput. Methodol., Numer. Heat Transfer, Part A, 1999, 36(3), 563–584.
9.
ShujaS. Z.YilbasB. S.Gas-assisted repetitive pulsed heating of a steel surface. Proc. Instn Meek. Engrs, Part C, Journal of Mechanical Engineering Science, 1998, 212(C8), 741–757.
10.
ShujaS. Z.Simulation of three-dimensional laser gas-assisted heating of solid substance: the Fourier heat conduction theory approach. PhD thesis, Mechanical Engineering Department, King Fahd University of Petroleum and Minerals, Dhahran, Saudi Arabia, June 1998.
11.
GotskiT. B.HussainiM. Y.LumleyJ. L.Simulation and Modeling of Turbulent Flows, 1996 (Oxford University Press, New York).
12.
IncroperaF. P.DewittD. P.Introduction to Heat Transfer—Appendix, 1985, pp. 667–696 (John Wiley, New York).
13.
PatankarS. V.Computer Analysis of fluid Flow and Heat Transfer, 1981, Ch. 8, pp. 223–252 (Pineridge, Swansea).
14.
ShujaS. Z.Calculations of fluid flow and heat transfer in expanding ducts. MSc thesis, King Fahd University of Petroleum and Minerals, Dhahran, Saudi Arabia, 1993.
15.
BatheK. J.Finite Element Procedures, 1996, Ch. 6, pp. 148–192 (Prentice-Hall, Englewood Cliffs, New Jersey).
16.
ShiuT. R.GrigoropoulosC. P.GreifR.Measurement of the transient glass surface deformation during laser heating. Trans. ASME, J. Heat Transfer, 1999, 121, 1042–1048.
17.
BerocciC.Introduction to the modeling of turbulence. Von Karman Institute for Fluid Dynamics, March 1991.
18.
ElhaleimO.ReggioM.CamateroR.Simulating two-dimensional turbulent flow by using k-ε model and the vorticity-stream function formulation. Int. J. Numer. Meth. in Fluids, 1992, 14, 961–980.
