**1. Introduction**

18 Advanced Topics in Measurements

Zahorik, P. (2000). Limitations in using Golay codes for head-related transfer function

The pendulum test is a means to evaluate the knee joint reflex from the pendulum motion induced by letting the lower leg drop freely after it has been lifted up (Watenberg, 1951). Many researchers have attempted to quantify the spinal cord stretch reflex from this pendulum motion in order to diagnose spasticity (Fowler et al., 2000; Kaeser et al., 1998; Lin & Rymer, 1991; Nordmark & Andersson, 2002; Stillman & McMeeken, 1995; Vodovnik et al., 1984). However, even today, much remains unknown about the relationship between this pendulum motion and the mechanism that produces the stretch reflex. For this reason, quantification studies on the stretch reflex have progressed slowly.

One method to advance the quantification of the stretch reflex may be to implement the following items in order:


We have already elucidated various phenomena following this procedure, but in this process, it has often been necessary to know angle, angular velocity, and angular acceleration values at arbitrary times during knee joint motion as initial and boundary conditions to solve nonlinear differential equations. Obtaining this kind of waveform with existing simple methods is difficult, as described below.

In principle, various existing sensors can be used to detect knee joint motion. However, several such sensors are not practical because of the knee joint's unique structural

Precise Measurement System

to estimate by any simple means.

knee joint motion in the pendulum test.

femur

posterior cruciate

knee joint; (b) Locus of axis of motion.

ligament

fibul

and lower leg mass.

for Knee Joint Motion During the Pendulum Test Using Two Linear Accelerometers 21

is the source that generates muscle contraction. The efferent fiber that controls it is not drawn. The knee joint oscillatory system consists of elasticity, viscosity, muscle contraction,

The above-mentioned quadriceps femoris muscle and hamstring muscle are the agonist and antagonist, respectively. When contractile force occurs in the agonist, the agonist shortens regardless of whether it is triggered consciously or unconsciously (when it is conscious, the antagonist also extends simultaneously), and consequently the knee extends. Similarly, the knee flexes when contractile force occurs in the antagonist. When conscious contractile force disappears or external forces that flex or extend the knee passively are eliminated, the lower leg will subsequently have damped oscillation with repeated flexion and extension unless it is resting in a stable position. In the following, we call such a dumped oscillation free one. Next, let us look at the movement of the knee joint rotation axis. In general the knee joint is classified as a uniaxial joint that performs flexion and extension movement, but strictly speaking its rotation axis, as described below, moves according to a complex mechanism in which the lower end of the femur slides while rolling along the top of the tibia (Kapandji, 1970). That is, though the position of the knee joint rotation axis seems as if it is fixed to the center of the disk, it slightly moves together with flexion or extension. The rotation axis that

The skeletal structure of the knee joint is shown in Fig. 2(a). The axis of motion during flexion and extension corresponds to the imaginary point where the collateral ligament and cruciate ligament intersect (shown with a black dot (●)). Fig. 2(b) shows the migration of the intersection. The uppermost and lowermost black dots are the positions of the axis of motion in full extension and full flexion, respectively. When the knee joint rotates from full extension toward flexion, the condyle of the femur moves by rolling only up to a certain angle, beyond which an element of incremental sliding begins to apply. At the vicinity of the maximum flexion, there is only sliding movement. The relationship between the amount of movement and the angle of the knee joint is therefore mechanically complex, and analyzing it quantitatively is not an easy task. Similarly, neither the position nor the trajectory is easy

For the above reasons, unlike the elbow and other joints, it is not easy to measure exactly the

evolute

axis of motion

moves based on this kind of phenomenon is called the axis of motion.

axis of motion

ligament

anterior cruciate

tibia

Fig. 2. Skeletal structure and locus of axis of motion of knee joint. (a) Skeletal structure of

(a) (b)

complexity. In addition, all existing sensors can measure only one of angle, angular velocity, or angular acceleration. Because of this, the only method that we can produce more than one type of waveform using such sensors is to differentiate and integrate the measured waveforms. As a result, it is difficult to ensure sufficient amplitude accuracy for waveforms obtained in this way and precise synchronization with measured waveforms.

For these reasons, we have recently begun investigating sensors that are suitable for the pendulum test. We have developed a new sensor that can precisely measure knee joint motion using two linear accelerometers. This article provides a comprehensive description of this sensor and related matters.

Section 2 briefly explains basic matters related to the pendulum test, such as the skeletal structure of the knee joint and the kinesiology of the stretch reflex. section 3 explains the measurement principle, assessment of accuracy in the laboratory, and the precision estimates when measuring subjects with the knee joint motion measurement system that is the main topic of this article. section 4 examines the results with the knee joint motion measurement system using these sensors; that is, the angle waveform and angular acceleration waveform of the knee joint in the pendulum test. We then touch briefly on a pendulum test simulator and an inverse simulation of measured waveform to more effectively utilize the results of the measurements, including the future outlook. section 5 provides a brief summary.
