**2.1 Structure of the knee joint**

The general motion of the knee joint is flexion and extension in the sagittal plane, caused consciously (actively) or unconsciously (passively). The leg structure that contributes to this motion is shown in Fig. 1.

Fig. 1. Mechanism of extension and flexion.

The disc located at the end of the femur represents the knee joint, and the center of the disc is the rotation axis of the knee joint. The lower leg is fixed to the disc. The upper and lower ellipses are the quadriceps femoris muscle and hamstring muscle, respectively. One end of each muscle is fixed on the circumference of the disc. The spring and dashpot drawn in each of these ellipses are the respective elasticity and viscosity of the muscle. The force generator

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

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

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

The general motion of the knee joint is flexion and extension in the sagittal plane, caused consciously (actively) or unconsciously (passively). The leg structure that contributes to this

quardriceps femoris muscle

force generator

elasticity

viscosity

femur knee joint

hamstring muscle

The disc located at the end of the femur represents the knee joint, and the center of the disc is the rotation axis of the knee joint. The lower leg is fixed to the disc. The upper and lower ellipses are the quadriceps femoris muscle and hamstring muscle, respectively. One end of each muscle is fixed on the circumference of the disc. The spring and dashpot drawn in each of these ellipses are the respective elasticity and viscosity of the muscle. The force generator

obtained in this way and precise synchronization with measured waveforms.

of this sensor and related matters.

provides a brief summary.

motion is shown in Fig. 1.

**2.1 Structure of the knee joint** 

**2. Biomechanics of the knee joint** 

Fig. 1. Mechanism of extension and flexion.

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, and lower leg mass.

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

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 to estimate by any simple means.

For the above reasons, unlike the elbow and other joints, it is not easy to measure exactly the knee joint motion in the pendulum test.

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

Precise Measurement System

by the third and fourth terms.

Fig. 4. Structure of muscle spindle.

commands.

approximation) (Harvey & Matthews, 1961).

shown in the figure.

for Knee Joint Motion During the Pendulum Test Using Two Linear Accelerometers 23

but they have a little influence on the stretch reflex in the pendulum test, and so it is not

The afferent signal of Group Ia fiber is given as follows as the impulse frequency *f*<sup>s</sup> (primary

Here, *x* is extrafusal muscle fiber (muscle) displacement, *f*γd and *f*γs are the respective impulse frequencies from the brain to phasic and tonic γ-motoneurons, and *k*1s, *k*1d, *k*2s, and *k*2d are constants. As shown in the above equation, there are two types of components in stimuli detected by the muscle spindle in the stretch reflex: a stretch velocity component expressed by the first and second terms, and a muscle displacement component expressed

nuclear chain intrafusal

static γ-fiber dynamic γ-fiber

muscle fiber

Commands to control the lower extremities are transmitted from the brain to muscle via the spinal cord. They are broadly divided into commands for flexion and extension, commands for maintaining of posture and commands for adjusting of the muscle spindle sensitivity. The first commands are generated only consciously, the second and third ones are generated consciously and/or unconsciously. Measurements of knee joint motion in the pendulum test are however done under the unconscious state of the subjects, and so the commands in this case are only unconscious ones to maintain posture and adjust the muscle spindle sensitivity. Consequently, the presence or absence of the efferent command toward the muscle and its strength during the pendulum test are determined only by these unconscious

Fig. 5 shows the reflex arcs in the pendulum test schematically with a focus on the quadriceps femoris muscle. It includes phasic γ-motoneuron, tonic γ-motoneuron and αmotoneuron that play principal roles in the stretch reflex. The upper part enclosed by the solid line is the spinal cord. Signals *f*e and *f*i are commands to determine the posture, and represent frequencies of the impulses from the brain to the α-motoneuron and presynaptic inhibition part, respectively. The presynaptic inhibition part usually suppresses afferent signal from the muscle spindle so that it does not reach the α-motoneuron. Signals *f*γd and *f*γ<sup>s</sup> are commands to adjust the muscle spindle sensitivity, and represent frequencies of the impulses from the brain to the phasic γ-motoneuron and tonic γ-motoneuron, respectively.

Gla fiber nuclear bag intrafusal

muscle fiber

**2.2.3 Phasic stretch reflex and tonic stretch reflex** 

(1)
