unknown user

02-23-1991, 12:03 PM

Dear BIOMCH-L readers,

In his discussion of the 'wobbling mass' model, Herman Woltring has

raised the question whether the assumption of fixed joint centers would

cause significant errors in the estimation of joint contact forces. I

think it will, because an essential step before joint forces are

calculated, is the calculation of muscle forces. This involves two

basic problems: the distribution criterion and the moment arms of the

muscles. The moment arms have usually been calculated with respect to a

fixed joint center, and we all know that such a thing does not exist in

the knee joint. Estimated forces will contain relative errors as large

as the error in the joint center location, divided by the moment arm.

An elegant way to get rid of fixed joint centers has been demonstrated

in the December (1990) issue of the Journal of Biomechanics by Cees Spoor

and co-workers from the University of Leiden, Netherlands. The

instantaneous moment arm of a muscle (conventionally defined as the

perpendicular distance from the line of action to the instantaneous

joint center) can also be defined as the partial derivative of the

muscle length with respect to the angle of the joint. So, you only need

to know how the length of a muscle depends on joint angles (from cadaver

measurements), and *not* the location of the actual joint center at each

instant in time. The method also solves another problem: that of a

muscle not following the shortest path from origin to insertion when it

curves around bone or other muscles. Conventional models have great

difficulty describing this.

If this principle (of virtual work) is also used to determine the

moment arm of an external (ground reaction) force, assumptions on the

kinematical properties of joints will no longer be a source of error in

inverse dynamics analysis. Inertial forces require some special

attention though.

Sometimes, e.g. in a 'forward' simulation, we *do* want to describe

exactly how the segments are kinematically coupled, but modern multibody

software packages (e.g. DADS) contain a rather extensive library of

kinematic connections.

-- Ton van den Bogert

Faculty of Veterinary Medicine

University of Utrecht

In his discussion of the 'wobbling mass' model, Herman Woltring has

raised the question whether the assumption of fixed joint centers would

cause significant errors in the estimation of joint contact forces. I

think it will, because an essential step before joint forces are

calculated, is the calculation of muscle forces. This involves two

basic problems: the distribution criterion and the moment arms of the

muscles. The moment arms have usually been calculated with respect to a

fixed joint center, and we all know that such a thing does not exist in

the knee joint. Estimated forces will contain relative errors as large

as the error in the joint center location, divided by the moment arm.

An elegant way to get rid of fixed joint centers has been demonstrated

in the December (1990) issue of the Journal of Biomechanics by Cees Spoor

and co-workers from the University of Leiden, Netherlands. The

instantaneous moment arm of a muscle (conventionally defined as the

perpendicular distance from the line of action to the instantaneous

joint center) can also be defined as the partial derivative of the

muscle length with respect to the angle of the joint. So, you only need

to know how the length of a muscle depends on joint angles (from cadaver

measurements), and *not* the location of the actual joint center at each

instant in time. The method also solves another problem: that of a

muscle not following the shortest path from origin to insertion when it

curves around bone or other muscles. Conventional models have great

difficulty describing this.

If this principle (of virtual work) is also used to determine the

moment arm of an external (ground reaction) force, assumptions on the

kinematical properties of joints will no longer be a source of error in

inverse dynamics analysis. Inertial forces require some special

attention though.

Sometimes, e.g. in a 'forward' simulation, we *do* want to describe

exactly how the segments are kinematically coupled, but modern multibody

software packages (e.g. DADS) contain a rather extensive library of

kinematic connections.

-- Ton van den Bogert

Faculty of Veterinary Medicine

University of Utrecht