User guide

Charnwood Dynamics Ltd. Coda cx1 User Guide – Advanced Topics III - 1

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Instead, its position varies with the geometry of body segments as they move relative to

each other and, to a lesser extent, with localised segment deformation. Yet the body’s

mass-centre is crucially important during free-flight (or free-fall) phases since its trajectory

is constrained to be parabolic in order to satisfy Newton’s laws of motion. (During free-fall

the body is subject only to the constant force of gravity, assuming drag forces to be

negligible.) Any activity in which the body loses contact with external objects involves

phases, however brief, of free-fall: apart from all types of jumping we include running,

diving and other gymnastics (sky-diving is not included on account of significant drag

forces!).

In the diagram below the stick figure depicts the human form in mid-somersault; limb

segment mass-centres are represented by weighted virtual markers whose positions have

already been defined by the methods described in the previous section.

The resultant virtual marker, located at P

, represents an instantaneous centre of mass

for the entire body, and is clearly external to the body in this instance. A co-ordinate

transform to this virtual marker would provide a convenient means of viewing all the

relative limb movements. The derivable parameters for the parabolic trajectory of P

would provide key measures for this type of activity.

Solving the localization of a known point into a rigid marker triad (second category)

This scenario is altogether more complicated. Given three markers to represent a rigid

body and one further, relatively fixed point of the body segment (where, for some reason,

we would be unable to track a real marker during dynamic acquisition with Coda), can we

represent that point as a virtual marker referenced to the other markers?

Indeed we can, but this entails finding such weights and a normal offset as would be

required to construct the location as described in secton 3. A fair approximation may be

found by trial and error but for a precise solution the following method is suggested. Since

the user may well find the mathematics rather unfriendly, a ready-made Microsoft Excel

spreadsheet solution is available from Charnwood Dynamics upon request.

The location of our point of interest, relative to well spaced (non co-linear) markers M

, M

and M

, may be determined during a ‘static acquisition’ with Coda wherein the subject,

whilst remaining static, is scanned in such a way as to allow additional markers, briefly, to

‘point’ to the location of interest. (It may be possible to place there, in-view, a fourth

marker during this acquisition; if not, the location will need to be a virtual marker

constructed from M

, M

, etc... using methods of section3.) Let this point of interest be

denoted by (static) position vector V

Shaded disks represent pre-determined virtual

markers at segment mass centres. The relative

weights are in proportion to body segment masses

and are illustrated by variation of disk size.