A passive resistance against rotation of a joint is called "joint passive resistance." This resistance is caused by the soft tissues around the joint such as ligaments, tendons, and articular capsule. It is often measured as moment around the joint according to the joint angle or angular velocity by rotating the joint without the activities of muscles.
The joint passive resistance is modeled as an elastic element like a torsion spring and a viscous element like a rotary damper. The elastic resistance effects largely at the limit of ROM. The viscous resistance effects constantly during motion. These two resistances are non-linear, but the viscous resistance is often approached as a linear function of the joint angular velocity.
These characteristics is important to estimate muscle load or fatigue during motion, especially in the field of biomechanics. In addition, some researches show that these resistances influence the basis of motion effectively.
The measuring methods of the joint passive resistances are classified broadly as follows: (1) estimation by quasi-static equilibration, (2) estimation by dynamic equilibration, (3) measurement of cadaver. Figure is shown the definitions of notations.
These are the methods which can estimate the joint elastic characteristics from the moment and the relative angle of the joint when the upper segment is fixed and the lower segment is rotated passively.
The rotational static equilibration formula on the vertical plane to the ground under the passive condition of a joint is shown as
This formula means that the moment by own weight of the lower segment subtracted from that by supporting force leaves the joint elastic moment. The joint angle is measured with a potentiometer or a motion capture. The supporting force is measured with a load cell, and the lower segment is rotated by a mechanical or man-powered method.
This method need the weight and the COG of the segment. These parameters are usually given by statistic methods, because these are difficult to measure directly. In this method, it is easy to fix the body of the subject.
Improving (1-1), the own weight is canceled by moving the joint on the parallel plane to the ground as
This method does not need the weight and the COG of the segment, but it is difficult to fix the body and to support the body posture of the subject, especially in the measurement of the lower extremities.
Using a torque meter is capable of measuring the joint passive moment. But, this method needs large devices, and the torque meter often obstructs the motion of joint as
Using a torque meter is capable of measuring the joint passive moment. But, this method needs large devices, and the torque meter often obstructs the motion of joint.
These methods have a common matter that the viscous resistance effects the motion in the case of the fast rotation of the lower segment. As a result, the measured characteristic often has hysteresis. However, these method is very easy to use, and it is also capable of measuring the viscous characteristic through this hysteresis.
These are classified into two methods. One is the expanded method of the quasi-static equilibration. The other is the impedance measurement method mainly used in robotics.
When a segment oscillates, the rotational motion formula around a joint is shown as
Adjusting the parameters of the spring and the force reaction point, this formula equals to as
The linear viscous coefficient is calculated from the extinction ratio of this oscillation.
This method needs moment of inertia which is difficult to estimate. In addition, when the joint is moved passively, to oscillate the segment is difficult because of the effect of the joint viscous resistance. Therefore, the method with the oscillation caused by an external force actively is also used.
Originally, this is a method that examines the dynamic characteristic of a robot arm. Mainly in case of upper extremities, when the segment is moved on the parallel plane to the ground and is acted an external torque, the motion formula is shown as
The time series parameters of the elastic and viscous coefficient, and moment of inertia are defined as each linear coefficients for the joint angle, the joint angular velocity, and joint angular acceleration. Using Laplace transform, these three parameters are redefined as linear coefficients for the angle during motion. These parameters are not constant during motion. This means that these are dynamic parameters including the effects of posture, not static parameters.
This method is directly measured from the cadaver. Especially, most of the parameters used in the analysis of car collision are from this method. The parameters tend to be stiffer than those from living because of cadaveric stiffening.
It is difficult to unify the definition of the joint angle. However, the definition of the rotational direction of the joint is almost the same, so in this HP, the direction of the joint angle and that of the joint passive resistance moment are unified regardless of any references.
Each direction of flexion, abduction, and lateral axial rotation is defined as positive, and that of extension, adduction, and medial axial rotation is defined as negative. Furthermore, the unit of the joint angle is the radian, not the degree.
Each resistance moment against extension, adduction, and medial axial rotation is defined as positive, and that against flexion, abduction, and lateral axial rotation is defined as negative. The formulas which definitions are different from that of this HP are considered to be adapted to this HP.