bsellers37

01-06-2010, 10:01 PM

Dear All,

I've just been playing with calculating moment arms in 3D simulations using the commonly used An 1984 approach of measuring the change in length of a muscle and dividing it by the angular change at a joint. This works fine but I'm not happy with the term 'moment arm' as it applies in this case. In 2D, moment arm is the perpendicular distance of the line of action of a force from the fulcrum. In 3D, as calculated using the delLen/delTheta formula this isn't the case at all. It will give the same answer if the line of action is at right angles to the axle but otherwise the value it gives is less (potentially very much less) than the perpendicular distance. In the extreme when the line of action is parallel to the rotation axis there is no change of length with change of angle and the result is zero. Mechanically this is obviously a very useful value to calculate since it is certainly the effective moment arm in terms of the torque generated by contraction of a muscle but I'm not sure that moment arm is the correct term. And if it isn't moment arm, then what is it. It could be something like the mechanical advantage but that should be probably unitless (force/force or distance/distance) and distance/angle doesn't quite fit. I'm sure there is a perfectly good term for this quantity (and it may indeed by moment arm - but if it is I shall have to change my lectures to say that the 2D case is actually a special case and doesn't apply in 3D which is tricky because there are plenty of 3D moment arm papers out there).

Hopefully someone can enlighten me.

Cheers

Bill

--

Dr. Bill Sellers Email: William.Sellers@manchester.ac.uk

Programme Director of Zoology Skype: wisellers

Faculty of Life Sciences Tel. 0161 2751719

The University of Manchester Fax: 0161 2753938

3.614 Stopford Building Mob: 0785 7655786

Oxford Road, Manchester, M13 9PT, UK http://www.animalsimulation.org

An KN, Takahashi K, Harrigan TP, Chao EY. 1984. Determination of muscle orientations and moment arms. J Biomech Eng 10:280–282.

I've just been playing with calculating moment arms in 3D simulations using the commonly used An 1984 approach of measuring the change in length of a muscle and dividing it by the angular change at a joint. This works fine but I'm not happy with the term 'moment arm' as it applies in this case. In 2D, moment arm is the perpendicular distance of the line of action of a force from the fulcrum. In 3D, as calculated using the delLen/delTheta formula this isn't the case at all. It will give the same answer if the line of action is at right angles to the axle but otherwise the value it gives is less (potentially very much less) than the perpendicular distance. In the extreme when the line of action is parallel to the rotation axis there is no change of length with change of angle and the result is zero. Mechanically this is obviously a very useful value to calculate since it is certainly the effective moment arm in terms of the torque generated by contraction of a muscle but I'm not sure that moment arm is the correct term. And if it isn't moment arm, then what is it. It could be something like the mechanical advantage but that should be probably unitless (force/force or distance/distance) and distance/angle doesn't quite fit. I'm sure there is a perfectly good term for this quantity (and it may indeed by moment arm - but if it is I shall have to change my lectures to say that the 2D case is actually a special case and doesn't apply in 3D which is tricky because there are plenty of 3D moment arm papers out there).

Hopefully someone can enlighten me.

Cheers

Bill

--

Dr. Bill Sellers Email: William.Sellers@manchester.ac.uk

Programme Director of Zoology Skype: wisellers

Faculty of Life Sciences Tel. 0161 2751719

The University of Manchester Fax: 0161 2753938

3.614 Stopford Building Mob: 0785 7655786

Oxford Road, Manchester, M13 9PT, UK http://www.animalsimulation.org

An KN, Takahashi K, Harrigan TP, Chao EY. 1984. Determination of muscle orientations and moment arms. J Biomech Eng 10:280–282.