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Technical Brief

# Instantaneous Screws of Weight-Bearing Knee: What Can the Screws Tell Us About the Knee Motion

[+] Author and Article Information
Alon Wolf

Biorobotics and Biomechanics Lab,
Faculty of Mechanical Engineering,
Technion, I.I.T,
Haifa 32000, Israel
e-mail: alonw@technion.ac.il

Contributed by the Bioengineering Division of ASME for publication in the Journal of Biomechanical Engineering. Manuscript received July 29, 2012; final manuscript received January 28, 2014; accepted manuscript posted March 6, 2014; published online May 16, 2014. Editor: Beth Winkelstein.

J Biomech Eng 136(7), 074502 (May 16, 2014) (7 pages) Paper No: BIO-12-1328; doi: 10.1115/1.4027055 History: Received July 29, 2012; Revised January 28, 2014; Accepted March 06, 2014

## Abstract

There are several ways to represent a given object's motion in a 3D space having 6DOF i.e., three translations and three rotations. Some of the methods that are used are mathematical and do not provide any geometrical insight into the nature of the motion. Screw theory is a mathematical, while at the same time, geometrical method in which the 6DOF motion of an object can be represented. We describe the 6DOF motion of a weight-bearing knee by its screw parameters, that are extracted from 3D Optical Reflective motion capture data. The screw parameters which describe the transformation of the shank with respect to the thigh in each two successive frames, is represented as the instantaneous screw axis of the motion given in its Plücker line coordinate, along with its corresponding pitch and intensity values. Moreover, the Striction curve associated with the motion provides geometrical insight into the nature of the motion and its repeatability. We describe the theoretical background and demonstrate what the screw can tell us about the motion of healthy subjects' knee.

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## Figures

Fig. 2

Markers setup on the thigh and shank (right: view from Vicon Nexus). Markers are arbitrarily placed.

Fig. 1

Screw motion (helical motion), A is the screw axis, q is the pitch

Fig. 3

Gait events [22]

Fig. 4

Markers trajectory-example 1, one group of markers attached to the thigh and the other to the shank

Fig. 10

Intensity values of screws—example 2

Fig. 11

Knee flexion/extension angle as given in Vicon Polygon report (example 1—left, example 2—right) left leg- higher second pic

Fig. 5

Striction curve—example 1 a close curve suggests a repeatable motion

Fig. 6

Striction curve—example 2

Fig. 7

Pitch values (upper) and screw axis distance (lower)—example 1. Zero values of pitch reflect a pure rotation motion

Fig. 8

Pitch values (upper) and screw axis distance (lower)—example 2

Fig. 9

Intensity values of screws—example 1 high values reflect high acceleration of the limb

Fig. 12

Knee angle during gait cycle [18]

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