Dear Biomch-L readers,

I have completed many 3D multi-segment rigid body models of the human body to

calculate the joint (F*v) and muscle powers (M*w) during human movement. I am

familiar with Winter's work who emphasised the usefulness of this approach in

biomechanics. He believed that a typical power analysis would show the distinct

patterns of energy generation and absorption by the muscles, and this could have

significant implications for training and conditioning.

Winter's calculations are relatively simple. In his book "Biomechanics and

Motor Control of Human Movement (2nd Ed, 1990), he intially stated that muscle

power is the produce to net muscle moment (M) and angular velocity (w) yielding

the formula P = Mw, where P is power in watts. This power could be therefore

positive or negative depending on whether the muscles were performing a positive

rate of change or negative change of work. Hence the terms muscle power

generation and muscle power absorption were conceptualised mechanically. A

little later on Winter says that the aforementioned formula should be modified

to include the angular velocities of the adjacent segments in order to partition

the transfer component so that w is repaced by (w1 - w2) and the muscle power

equation now becomes P=M(w1-w2), where if w1 and w2 have the same polarity, the

rate of transfer is the lesser of the two power components.

In Zajac et al. (2002). Biomechanics and muscle coordination of human walking.

Part 1: Introduction to concepts, power transfer, dynamics and simulations. Gait

and Posture 16 (2002), 215-232, states the following:

(i) any one muscle may effect the acceleration and power of ALL body segments

because of dynamic coupling.

(ii)the net power instantaneously delivered by a muscle to either the segment of

origin or insertion must be found from COUPLED EQUATIONS OF MOTION and cannot be

found from the dot product of its force vector at the origin (insertion) with

the velocity vector of the origin (insertion) OR from the dot product of the net

joint moment vector with the segment angular velocity vector. The reason is that

the effects of the contributions of net joint moment to the joint intersegmental

forces and the muscle contributions to joint intersegmental forces are not

included.

(iii) It is often erroneously stated that or inferred that a muscle delivers

power to or absorbs power from only the segments to which it attaches.

(iv) This error (iii) seems to arise because of the lack of recognition that the

terms in the coupled dynamic equations are correct for computing muscle power to

the entire sustem, but incorrect when used separately to find the net

contribution to the segments to which they attach.

Therefore, I have the following questions that I would like resolved:

(a) From the inverse dynamics solution of two or more coupled rigid bodies, what

would the value of just the net joint torque multiplied the corresponding

segment angular velocity compute (i.e. just P = Tw)? Anything meaningful?

(b) If the net joint torque (from inverse dynamics) multiplied by the difference

in angular velocities of the adjacent segments was calculated would this

satifactorily give the values of THE TOTAL SUM OF active muscle power flows in

or out of the segment (i.e. P=T(w2-w1)). Is this always necessary or could

sometimes P=Tw used?

(c) Can joint muscle power or absorption be calculated accurately using Winter's

approach using the joint torques found from an inverse dynamics solution? Is

this what Winter meant or did he mean as in (ii) above? Is the methodology for

calculating power flows correct in Winter?

(d) Can the power flow equations easily applied to the 3D case since power is a

scalar quantity?

(e) How should power flows into or out of a segment be described taking into

account statement (iv) by Zajac et al. Does this mean that P=T(w2-w1) give the

net joint power which represents the SUMMED power by the net joint moment

to/from ALL the segments?

Your replies would be greatly appreciated, and a summary of replies posted.

Thank you.

Rene Ferdinands

Department of Physics &

Electronic Engieering

University of Waikato

Hamilton

New Zealand

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I have completed many 3D multi-segment rigid body models of the human body to

calculate the joint (F*v) and muscle powers (M*w) during human movement. I am

familiar with Winter's work who emphasised the usefulness of this approach in

biomechanics. He believed that a typical power analysis would show the distinct

patterns of energy generation and absorption by the muscles, and this could have

significant implications for training and conditioning.

Winter's calculations are relatively simple. In his book "Biomechanics and

Motor Control of Human Movement (2nd Ed, 1990), he intially stated that muscle

power is the produce to net muscle moment (M) and angular velocity (w) yielding

the formula P = Mw, where P is power in watts. This power could be therefore

positive or negative depending on whether the muscles were performing a positive

rate of change or negative change of work. Hence the terms muscle power

generation and muscle power absorption were conceptualised mechanically. A

little later on Winter says that the aforementioned formula should be modified

to include the angular velocities of the adjacent segments in order to partition

the transfer component so that w is repaced by (w1 - w2) and the muscle power

equation now becomes P=M(w1-w2), where if w1 and w2 have the same polarity, the

rate of transfer is the lesser of the two power components.

In Zajac et al. (2002). Biomechanics and muscle coordination of human walking.

Part 1: Introduction to concepts, power transfer, dynamics and simulations. Gait

and Posture 16 (2002), 215-232, states the following:

(i) any one muscle may effect the acceleration and power of ALL body segments

because of dynamic coupling.

(ii)the net power instantaneously delivered by a muscle to either the segment of

origin or insertion must be found from COUPLED EQUATIONS OF MOTION and cannot be

found from the dot product of its force vector at the origin (insertion) with

the velocity vector of the origin (insertion) OR from the dot product of the net

joint moment vector with the segment angular velocity vector. The reason is that

the effects of the contributions of net joint moment to the joint intersegmental

forces and the muscle contributions to joint intersegmental forces are not

included.

(iii) It is often erroneously stated that or inferred that a muscle delivers

power to or absorbs power from only the segments to which it attaches.

(iv) This error (iii) seems to arise because of the lack of recognition that the

terms in the coupled dynamic equations are correct for computing muscle power to

the entire sustem, but incorrect when used separately to find the net

contribution to the segments to which they attach.

Therefore, I have the following questions that I would like resolved:

(a) From the inverse dynamics solution of two or more coupled rigid bodies, what

would the value of just the net joint torque multiplied the corresponding

segment angular velocity compute (i.e. just P = Tw)? Anything meaningful?

(b) If the net joint torque (from inverse dynamics) multiplied by the difference

in angular velocities of the adjacent segments was calculated would this

satifactorily give the values of THE TOTAL SUM OF active muscle power flows in

or out of the segment (i.e. P=T(w2-w1)). Is this always necessary or could

sometimes P=Tw used?

(c) Can joint muscle power or absorption be calculated accurately using Winter's

approach using the joint torques found from an inverse dynamics solution? Is

this what Winter meant or did he mean as in (ii) above? Is the methodology for

calculating power flows correct in Winter?

(d) Can the power flow equations easily applied to the 3D case since power is a

scalar quantity?

(e) How should power flows into or out of a segment be described taking into

account statement (iv) by Zajac et al. Does this mean that P=T(w2-w1) give the

net joint power which represents the SUMMED power by the net joint moment

to/from ALL the segments?

Your replies would be greatly appreciated, and a summary of replies posted.

Thank you.

Rene Ferdinands

Department of Physics &

Electronic Engieering

University of Waikato

Hamilton

New Zealand

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To unsubscribe send SIGNOFF BIOMCH-L to LISTSERV@nic.surfnet.nl

For information and archives: http://isb.ri.ccf.org/biomch-l

---------------------------------------------------------------