In this contribution, the kinematic angular and linear third-order properties, also known as jerk analysis, of a multi-body system are determined applying the concept of helicoidal vector fields. The reduced acceleration state, or accelerator, of the body of interest, with respect to a reference frame, is obtained as the time derivative, via a helicoidal field, of the velocity state, also known as the infinitesimal twist. Following that trend, the reduced jerk state, or jerkor, is obtained as the time derivative of the accelerator. The computation of the instantaneous centre of jerk, with its corresponding ellipsoid of jerk, is also included. The expressions thus obtained are extended systematically to multi-body systems. Two numerical examples are provided in order to illustrate the potential of the presented method.
SuhC. H.Higher order analysis of spatial coupler curves. J. Mech., 1971, 6, 81–95.
2.
SchotS. H.Jerk: The time rate of change of acceleration. Am. J. Phys., 1978, 46, 1090–1094.
3.
ŽefranM.KumarV.CrokeC.On the generation of smooth three-dimensional rigid body motions. IEEE Trans. Robot. Autom., 1995, 14, 579–589.
4.
ChengW.-T.Synthesis of universal motion curves in generalized model. ASME J. Mech. Des., 2002, 124, 284–293.
5.
MorassoP.Spatial control arm movements. Expl. Brain Res., 1981, 42, 223–227.
6.
FlashT.HoganN.The coordination of arm movements: An experimentally confirmed mathematical model. J. Neurosci., 1985, 5, 1688–1703.
7.
UnoY.KawatoM.SuzukiR.Formation and control of optimal trajectory in human multijoint arm movements. Biol. Cybern., 1989, 61, 89–101.
8.
CrossmanE. R. F. W.GoodeveP. J.Feedback control of handmovements and Fitts' law. Q. J. Expl. Psychol., 1983, A35, 251–278.
9.
GielenC. C.VrijenhockE. J.NeggersS. F.Arm position constraints during pointing and reaching in 3-D space. J. Neurophysiol., 1997, 78, 660–673.
10.
GoldvasserD.McGibbonC. A.KrebsD. E.High curvature and jerk analyses of arm ataxia. Biol. Cybern., 2001, 84, 85–90.
11.
NovakK. E.MillerL. E.HoukJ. C.Kinematic properties of rapid hand movements in a knob turning task. Expl. Brain Res., 2000, 132, 419–433.
12.
VivianiP.SchneiderR.A development study of the relationship between geometry and kinematics in drawing movements. J. Expl. Psychol. Hum. Percept. Perform., 1991, 17, 198–218.
13.
VivianiP.FlashT.Minimum-jerk, two-thirds power law, and isochrony: Converging approaches to movement planning. J. Expl. Psychol. Hum. Percept. Perform., 1995, 21, 32–53.
14.
ZahraeeM. A.NeffG. P.Computer-aided analysis of cam mechanisms: A reverse engineering approach. In Proceedings of the Second International Mechanical Engineering Conference, Shiraz, Iran, 1996, pp. 905–912.
15.
NguyenV.-U.KimD.Cam profile smoothing by modified spline curves. In Proceedings of the 12th IFToMM World Congress, Besancon, France, 2007.
16.
LeeT. S.LinY. J.An improved sculptured part surface design method with jerk continuity consideration for smooth machining. Int. J. Adv. Manuf. Technol., 1999, 15, 640–648.
17.
ErkorkmazK.AltintasY.High speed CNC system desing. Part I. Jerk limited trajectory generation and quintic spline interpolation. Int. J. Mach. Tools Manuf., 2001, 41, 1323–1345.
SparisP. D.MoroutsosS. G.A new matrix method for the kinematic analysis and motion simulation of planar mechanisms with lower kinematic pairs. ASME J. Mech. Trans. Autom. Des., 1984, 106, 429–436.
20.
UrbinatiF.PennestriE.A tool for third order kinematic analysis of spatial mechanisms. In Proceedings of the 25th Biennial Mechanisms Conference, Atlanta, Georgia, 1998, paper DETC/MECH-5901 (available on CD-ROM).
21.
FeatherstoneR.The acceleration vector of a rigid body. Int. J. Rob. Res., 2001, 20, 841–846.
22.
KumarV. R.WaldronK. J.Force distribution in closed kinematic chains. IEEE Trans. Robot. Autom., 1988, 4, 657–644.
23.
KaneT. R.LevinsonD. A.Dynamics: Theory and applications, 1985 (McGraw Hill, New York).
