Mass: m
Length, distance: l
Time: (l/g)^1/2
Cadence: (g/l)^1/2
Velocity: (g.l)^1/2
Acceleration: g
Force: m.g
Moment: m.g.l
Work: m.g.l
Power: m.(g)^3/2.(l)^1/2
Angle: (already dimensionless)
Angular Velocity: (g/l)^1/2
Angular Acceleration: g/l
Moment of Inertia: m.l^2
where m = body mass, l = lower-limb length (hip-joint to floor) and
g = gravitational constant (9.81 ms^2)
To those interested in the normalization issue, I can advertize here my Letter to the Editor in Gait and Posture: "Scaling Gait Data to Body Size", vol. 4 : 222 - 223. I received it just the other day. It is preceded by a paper by Zijlstra, Prokop and Berger (4: 212 - 221) and an editorial by D.Sutherland(4: 209 - 211), all related to the normalization subject. Your quest for normalized data for joint moments, work etc is certainly very relevant. I have some scattered data on this point, all expressed in dimensionless quantities s' = s/l , W' = W/mgl etcetera. >From Hof, Geelen and Van den Berg, " Calf muscle moment, work and efficiency in level walking" J Biomech 16: 523 - 537 (1983): Preferred steplength s' at an imposed speed v' s' = 1.1 v'^1/2 +- 0.2 negative work at ankle, Winter's A1 W-' = (2.91 +- 0.52 ) * 0.01 (independent of speed or steplength) >From Hof et al. "Calf muscle work and segment energy changes in humen treadmill walking", J. Electromyogr. Kinesiol. 2: 203 - 216 (1993): positive work at ankle, Winter's A2 W+' = 0.046 s'^2 (dependent on steplength only). kinetic+potential energy of swing leg E' = 0.23 v'^2 Data that relate joint moments, work, etc to speed are very relevant indeed as a reference in patient research, because these people usually walk at speeds far below "normal". Gait labs with those nice VICONs or ELITEs and undergraduate students should have no problem to gather these data from normal subjects! We - that is our Laboratory of Human Movement Analysis- are in the process of preparing EMG data obtained at walking speeds between 0.5 and 2 m/s. If there is interest we can post them when ready.
To show the power of this normalization follows here a table with data from Table 2.3 in Rose et al. Human Walking (2nd ed. of Inman). It gives preferred speed and cadence as a function of age. Leg length is from the original source, the book of Sutherland. leg NORMALIZED age cadence length speed stride cadence velocity (yr) (st/min) (m) (m/s) S/L 1.00 176 0.32 0.63 1.36 0.53 0.36 1.50 171 0.36 0.71 1.39 0.54 0.38 2.00 156 0.39 0.71 1.41 0.52 0.37 2.50 156 0.41 0.80 1.49 0.53 0.40 3.00 154 0.44 0.86 1.51 0.55 0.41 3.50 160 0.47 0.99 1.59 0.58 0.46 4.00 152 0.49 0.99 1.58 0.57 0.45 5.00 154 0.53 1.08 1.58 0.60 0.47 6.00 146 0.57 1.09 1.57 0.59 0.46 7.00 143 0.62 1.15 1.57 0.60 0.47 adult 111 1.00 1.45 1.57 0.59 0.46 It is clearly seen that the normalized quantities are essentially unchanged above age 3 1/2. Greetings from NL,At Hof Department of Medical Physiology University of Groningen Bloemsingel 10 NL-9712 KZ GRONINGEN The Netherlands Phone: (31) 50 3632645 Fax: (31) 50 3632751 (14 June 1996)Email your comments to
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