Northwestern University Feinberg School of Medicine

Northwestern University Prosthetics-Orthotics Center

Roll-over Shape Concept

The basic premise of the roll-over shape measurement can be illustrated using a simple rolling wheel (see Figure 1). As the wheel rolls it utilizes a series of contact points. These points, if measured in a world-based coordinate system, are in a straight line on the rolling surface (see Figure 1A). If these same contact points are measured relative to a coordinate system fixed on the wheel (i.e. a wheel-based coordinate system), the points indicate the rolling geometry or cam-shape of the wheel (see Figure 1B) . In the example of the rolling wheel, the wheel is rigid and the shape could easily be found instead by direct measurement of the wheel (e.g. tracing the outline of the wheel onto a piece of paper). However, the strength of this methodology is that it can be applied to a deformable object (e.g. a prosthetic foot) or a system comprised of deformable objects as well as active and passive mechanical linkages (e.g. a non-disabled ankle-foot system) to determine the effective rocker geometry that the combined effects of the system conform to create. In the case of deformable objects, the contact is often over a surface and not at one point only. However, the effective rocker geometry can be estimated by using the center of pressure of force as the contact point, the point that represents the net effect of the distributed pressure on the contact surface.

Simple rolling wheel used to illustrate the rollover shape concept.

To find the roll-over shape of the ankle-foot system, for example, we transform center of pressure data from a laboratory coordinate system into a shank-based coordinate system (see Figure 2) . The shank-based coordinate system is based on the ankle and knee markers and lies in the sagittal plane (newer measurements place the coordinate axes within a plane defined by the long axis of the foot and a line connecting the ankle and knee centers). This concept can be extended to three-dimensions to estimate effective rolling surfaces.

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Ankle-foot roll-over shape calculations in world-based coordinate systemMove the Mouse Pointer Over the Image to View the Animation of the Roll-Over Shape in Shank-Based Coordinates
Figure 2: [Modified from Hansen et al., 2004] Ankle-foot roll-over shape calculation [data taken from Winter, 1990]. (A) ankle and knee trajectories in the sagittal plane and center of pressure (CoP) on the floor. Data are in a laboratory-based coordinate system. (B) Data are transformed into a shank-based coordinate system. The CoP in shank-coordinates draws out the effective rocker, or roll-over shape, that the ankle and foot conform to between heel contact (HC) and opposite heel contact (OHC) events. Data in both plots are shown in green from HC to OHC and in red after OHC. Note the rocker shape between HC to OHC.

The roll-over shape is not a literal shape. In other words, the system does not conform to the complete roll-over shape at any one point in time (unless it is completely rigid like the wheel). Rather the shape is developed throughout the stance portion of the walking cycle. Figure 3 shows the average ankle-foot roll-over shape from 24 able-bodied subjects walking between 1.2 and 1.6 meters/second (Hansen et al., 2004).

References

Hansen, A., Childress, D., Knox, E. (2004) Roll-over Shapes of Human Locomotor Systems: Effects of Walking Speed. Clinical Biomechanics, Vol. 19, No. 4, 407-414.

Winter D., 1990. Biomechanics and Motor Control of Human Movement. Jon Wiley and Sons, Inc., Toronto.