JP2010193977A - Method for measuring mass and gravity center of each part of human body - Google Patents

Abstract

<P>PROBLEM TO BE SOLVED: To provide a method for measuring the mass and the gravity center of each part of every individual. <P>SOLUTION: The method for measuring the mass and the gravity center of each part of a human body includes the first step of setting a measurement point on a part of a subject, the second step of intermittently measuring displacement x<SB>i</SB>of the measurement point from a reference posture and a moment M around an optional point while changing the posture of the part on which the measurement point is set, the third step of estimating the mass m<SB>i</SB>of the measurement point of the part by means of multiple regression analysis using a formula M/g=Σm<SB>i</SB>x<SB>i</SB>+m'x', the fourth step of acquiring the mass of the part from the sum of the mass m<SB>i</SB>of the measurement points, and the fifth step of acquiring the gravity center of the part from the mass m<SB>i</SB>and the positions of the measurement points. In the method, the steps are carried out one by one. Because the mass and the gravity center of the part of the subject is thus measured directly, the mass and the gravity center of each part of every individual is measured accurately without relying upon statistical data. <P>COPYRIGHT: (C)2010,JPO&INPIT

Description

  The present invention relates to a method for measuring a mass and a center of gravity of each part of a human body. More specifically, the present invention relates to a method for measuring the mass and center of gravity of each part of the human body that can be measured for each individual without relying on statistical data.

In the medical field and sports kinematics field, it is very important to estimate the moment (joint moment) that acts on the joints of the human body during exercise. For example, muscle tension is estimated from the estimated joint moment using a musculoskeletal model.
In order to estimate the joint moment, it is necessary to measure the mass, center of gravity, and moment of inertia for each part of the human body. This is because the joint moment can be estimated from the measured mass and the like, the acceleration acting on each part of the human body during exercise, and the angular acceleration around the joint.
Conventionally, in order to measure the mass, the center of gravity, and the moment of inertia for each part of the human body, there is no method for individual measurement, and therefore, estimation is performed using statistical data obtained from anatomy or the like.
However, because there are individual differences in the mass of each part of the human body, etc., it should be measured for each individual, and if statistical data is used, accurate joint moments for each individual cannot be estimated. There is.

  On the other hand, there is Patent Document 1 as a conventional technique for measuring the mass of each part of the human body for each individual. The measurement method of Patent Document 1 is a part-by-part mass measurement method that measures the mass of each of the six parts of the head, the trunk, the left and right arms, and the left and right legs. Correspondingly, a plate-like mass measuring device is placed on the floor, and the person to be measured lies in the supine position or prone position on it, and measures the mass of each part.

However, in the measurement method of Patent Document 1, each part is affected by other parts connected by a joint, and when the force is applied to the joint, the mass of each part cannot be measured accurately. There's a problem.
Moreover, since it is necessary to prepare a measuring apparatus for every site | part, there exists a problem that it is difficult to measure the mass of a small site | part.
Furthermore, there is a problem that the center of gravity and the moment of inertia of each part cannot be measured, and the joint moment cannot be estimated by this alone.

JP 2007-212411 A

  In view of the circumstances described above, an object of the present invention is to provide a method for measuring the mass and the center of gravity of each individual part.

The method for measuring the mass and the center of gravity of each part of the human body according to the first aspect of the invention includes a first step of setting a measurement point on the assumption that the mass of the part is concentrated on the part of the subject, The posture x is changed only for the part where the measurement point is set, based on the displacement x _i from the reference posture (i indicates the number of the measurement point) and the moment M applied by the entire body of the measurement subject around any point. A second step of intermittently measuring while
M / g = Σm _i x _i + m'x '
(G is gravitational acceleration, m _i is the mass of the measurement point, m ′ is the mass of the subject other than the measurement point, x ′ is the distance from the arbitrary point of the center of gravity of m ′, and Σ is the sum of the measurement points Show.)
Heavy using equation from data obtained by the second step, the mass m _i at the measuring point of the site, which dependent variable M / g, independent variable x _i, the m _i and the partial regression variables fifth determining a third step of estimating the regression analysis, and a fourth step of obtaining the mass of said portion from the sum of the mass m _i of the measurement point, the center of gravity of the region from the mass m _i and the position of the measuring point Steps are sequentially performed.
The method for measuring the mass and the center of gravity of each part of the human body according to the second invention is characterized in that, in the first invention, in the first step, two measurement points are set for one part.
The method for measuring the mass and the center of gravity of each part of the human body of the third invention is characterized in that, in the first invention, in the first step, three measurement points are set for one part.
In the method for measuring the mass and the center of gravity of each part of the human body according to the fourth invention, in the first invention, in the first step, four or more measurement points are set so as not to be on the same plane for one part. It is characterized by that.
The method for measuring the mass and the center of gravity of each part of the human body according to the fifth invention is characterized in that, in the first invention, in the first step, measurement points are set only for one part.
According to a sixth aspect of the present invention, in the method for measuring the mass and the center of gravity of each part of the human body according to the first aspect of the present invention, measurement points are set at a plurality of parts in the first step.
According to a seventh aspect of the present invention, in the first invention, the vertical floor reaction force is measured in the second step, and the vertical floor reaction force is a reference value in the third step. If it is larger or smaller than this, it is removed from the data used for the multiple regression analysis.
According to an eighth aspect of the present invention, in the method for measuring the mass and the center of gravity of each part of the human body, in the second step, the moment M is defined as the center of gravity of the floor reaction force of the measurement subject in the reference posture. , A moment applied by the whole body of the person around the reference point, and in the third step,
M / g = Σm _i x _i
Using the formula, and estimates the mass m _i at the measuring point of the site.
The method for measuring the mass and the center of gravity of each part of the human body of the ninth invention is the first invention, in the third step,
(dM / dt) / g = Σm _i (dx _i / dt)
(DM / dt is the time derivative of moment M, and dx _i / dt is the time derivative of displacement x _i .)
Using the formula, and estimates the mass m _i at the measuring point of the site.
According to a tenth aspect of the present invention, in the first invention, in the first invention, in the first step, the measurement points are set in all the parts of the subject, and in the third step
_{M / g = Σm i x i} + (F z -Σm i) x N
(F _Z is the vertical floor reaction force, N is the number of measurement points, and Σ is the sum of measurement points other than the Nth measurement point.)
Using the formula, and estimates the mass m _i at the measuring point of the site.

According to the first invention, since the mass and the center of gravity of the part of the person to be measured can be directly measured, the mass and the center of gravity for each part can be accurately measured without relying on statistical data. .
According to the second invention, since two measurement points are set for one part, the position of the center of gravity on the line connecting the two measurement points is obtained from the measurement result of the mass of the measurement point. be able to.
According to the third invention, since three measurement points are set for one part, it is determined from the measurement result of the mass of the measurement point which position on the plane made up of the three measurement points is located at the center of gravity. Can be sought.
According to the fourth invention, since four or more measurement points are set for one part, the position of the center of gravity in the three-dimensional space is obtained from the measurement result of the mass of the measurement point. Can do.
According to the fifth aspect, since the measurement point is set only in one part, the measurement apparatus becomes simple, and the mass and the center of gravity can be easily obtained from the measurement data.
According to the sixth aspect of the invention, since measurement points are set at a plurality of parts, the mass and the center of gravity of many parts can be obtained in a short time.
According to the seventh aspect, since measurement data when the measurement subject is not sufficiently static can be removed from the multiple regression analysis, the mass of the measurement point can be estimated more accurately.
According to the eighth invention, since one partial regression variable can be eliminated by making M a moment applied by the entire body of the subject around the reference point, the accuracy of the multiple regression analysis can be improved. Can do.
According to the ninth aspect, the term of the mass m ′ of the person to be measured other than the measurement point can be deleted by differentiating, and one partial regression variable can be deleted. Can be improved.
According to the tenth invention, by erasing the section m _N, since the partial regression variable may be erased one, it is possible to improve the accuracy of the multiple regression analysis.

It is explanatory drawing of the typical measuring apparatus used for the measuring method which concerns on this invention. It is explanatory drawing at the time of attaching a marker to a forearm. It is explanatory drawing at the time of attaching a marker to a palm. It is explanatory drawing at the time of attaching a marker to a head. It is explanatory drawing of the measuring method which concerns on this invention. It is explanatory drawing of the measuring method. The human body other than the measurement site is omitted.

(measuring device)
Next, a typical measuring apparatus used in the measuring method according to the present invention will be described with reference to the drawings.
As shown in FIG. 1, a typical measuring device used in the measuring method according to the present invention is mainly composed of a floor reaction force meter and a three-dimensional motion analysis device.

The floor reaction force meter is composed of a strain gauge, a piezoelectric element, etc. When the person to be measured gets on the floor reaction force meter, the magnitude and direction of the floor reaction force applied to the person to be measured, or the floor reaction force It is a load sensor that can measure the center of gravity (weighted center). Some floor reaction force meters can measure the floor reaction force in the vertical, longitudinal, and left-right directions, but the floor reaction force meter used in the present invention measures at least the floor reaction force in the vertical direction and the weighted center. Anything that can be done.
Here, the floor reaction force means the force that the human body receives from the floor, and the magnitude of the force at rest is equal to the magnitude of the force with which the human body pushes the floor due to weight. The floor reaction force has a distribution on the contact surface between the floor and the human body, and the center of gravity of the distribution of the floor reaction force is the weighted center.

  The three-dimensional motion analysis device is a three-dimensional position measurement device that mainly includes a three-dimensional motion analysis camera and an electronic computer that performs image analysis, and measures the three-dimensional position of a marker attached to the body of the measurement subject. In general, the position, velocity, and acceleration of each marker are obtained by shooting the motion of the person to whom the marker is attached using multiple 3D motion analysis cameras and analyzing the video with software embedded in an electronic computer. And so on.

  The coordinates of the three-dimensional position may be set arbitrarily, but for the sake of simplicity, in the following, the surface of the floor reaction force meter is used as a reference, and the x axis, y axis, z Set the axis. The origin may be arbitrarily set according to the three-dimensional position measuring device, for example, the corner of the floor reaction force meter.

In the measurement method according to the present invention, it is necessary to intermittently acquire data from the floor reaction force meter and the three-dimensional motion analysis device at the same timing. This is because, as will be described later, it is necessary to measure the floor reaction force and the three-dimensional position with respect to one posture of the measurement subject, and it is necessary to measure in a plurality of postures.
Therefore, a control device (not shown) for controlling the floor reaction force meter and the three-dimensional motion analysis device and collecting data, and an electronic computer (not shown) for analyzing the collected data by a method described later are required. Depending on the use.

(Measurement method for one part)
Next, an embodiment of the present invention will be described with reference to the drawings.
Since the method of measuring the mass and the center of gravity of one part is fundamental, the embodiment will be described first.

[First step marker setting]
First, a marker for a three-dimensional motion analysis apparatus is attached to one part measured by the measurement subject. As will be described later, assuming that the mass of the part is concentrated at the position of the marker, the mass of each marker position is measured, and the mass of the part is calculated from the sum of the masses of the marker positions. The center of gravity of the part is obtained from the distribution of the masses.
In the present embodiment, the marker position corresponds to a “measurement point” described in the claims.

In order to obtain the center of gravity of a part, it is necessary to attach at least two markers to one part.
As shown in FIG. 2, for example, when measuring the forearm, the forearm is a beam-like member, and its center of gravity is expected to be on the axis of the beam, so markers are placed near the elbow and the wrist. Just attach it. From the measurement result of the mass at the marker position, it is possible to determine which position on the line connecting the two markers has the center of gravity.

  Also, as shown in FIG. 3, when measuring a planar part such as a palm, the center of gravity is expected to be on the plane, so it is only necessary to attach three markers. From the measurement result of the mass at the marker position, it is possible to determine which position on the plane composed of the three markers has the center of gravity.

  Or as shown in FIG. 4, when measuring the three-dimensional site | part like a head, what is necessary is just to attach a marker so that it may not become on the same plane at least four places. By attaching four markers, it is possible to determine which position in the three-dimensional space has the center of gravity from the measurement result of the mass of the marker position.

  Of course, four markers may be attached to a beam-like or planar part. Further, four or more markers may be attached to one part.

Note that the position of the center of gravity in the three-dimensional space can also be obtained by attaching three markers and setting the number of times of measurement to two. In this case, first, three markers are attached to the site to be measured, and the position of the center of gravity on a plane (for example, a vertical plane) made of the three markers is obtained. Next, the position of the marker is changed, and the position of the center of gravity on a new plane (for example, a horizontal plane) composed of the three markers is obtained again. It is possible to obtain the center of gravity in the three-dimensional space from the position of the center of gravity obtained at the first time and the position of the center of gravity obtained at the second time.
That is, the center of gravity position in the three-dimensional space can be obtained by attaching three markers to a three-dimensional part, not limited to a planar part.

  Since the number and position of suitable markers differ depending on the part to be measured, it is only necessary to select an optimal marker attachment method for each part in consideration of measurement accuracy of mass and center of gravity.

[2nd step: Measurement of marker position and moment]
Next, the person to be measured gets on the floor reaction force meter and slowly moves only the part where the marker is attached so that the acceleration is sufficiently smaller than the gravitational acceleration. At the same time, the position of the marker is measured with a three-dimensional motion analyzer. The floor reaction force is measured with a floor reaction force meter. The measurement data of the marker position and floor reaction force are collected intermittently while changing the posture of the part. That is, the posture of the part to be measured is changed variously, and the floor reaction force and the position of the marker for each posture are measured.

  In addition, as shown in FIG. 1, the person to be measured may be sitting on a chair on the floor reaction force meter or standing while measuring.

[Third step: Estimating the mass of the marker position]
Next, the mass at each marker position is estimated from the collected measurement data.
As shown in FIGS. 5 and 6, the posture at the start of measurement of the part to be measured is set as a reference posture, and the center of gravity position (weighted center) of the floor reaction force of the measurement subject in the reference posture is set as a reference point. Note that the reference posture need not be the posture at the start of measurement, and may be set to an arbitrary posture measured at an arbitrary timing according to the convenience of measurement. This is because, as will be described later, it is only necessary to measure the displacement of the marker position from the reference posture and the displacement of the weighted center from the reference point. The “reference posture” described in the claims means an arbitrary reference posture.

また、各マーカー位置の質量をm_i、各マーカーの基準姿勢からのx軸方向の変位をx_i、y軸方向の変位をy_iとすると次式も成り立つ。

ここでiは部位におけるマーカーの番号であり、その部位にNか所のマーカーを取り付けた場合、i=1,2,・・・,Nである。また、gは重力加速度である。 If the displacement in the x-axis direction from the reference point is x _G , the displacement in the y-axis direction is y _G and the vertical floor reaction force at that time is F _z , the weighted center when the posture changes is assumed to be around the reference point. the moment exerted by the entire body of the person to be measured x component M _x, y component M _y is given by the following equation.

Further, when the mass at each marker position is m _i , the displacement in the x-axis direction from the reference posture of each marker is x _i , and the displacement in the y-axis direction is y _i , the following equation is also established.

Here, i is the number of the marker at the site, and when N markers are attached to the site, i = 1, 2,..., N. G is the gravitational acceleration.

Formula 3, M _x in Formula 4, M _y measurement data of force plate, i.e. x _G, y _G, obtained from F _z, x _i, y _i is obtained from the measurement data of the three-dimensional motion analysis apparatus . _{Accordingly, M x / g, M y} / g a dependent variable, x _i, independent variables y _i, if the partial regression coefficients m _i, is possible to estimate the mass m _i of each marker position by multiple regression analysis it can.

Yの実測値y_k（k=1,2,・・・,n n:測定データ数）と、X_iの実測値から式５で与えられる予測値Y_k（k=1,2,・・・,n n:測定データ数）との差（残差）e_kの二乗和Qが最小になるような偏回帰係数b_iを求める方法である。

また、重回帰分析で求められた偏回帰係数の確からしさは、重相関係数などの値で表わされる。 Here, multiple regression analysis is used when the following relationship is expected to be established between the independent variable X _i (i = 1, 2, ..., NN: the number of independent variables) and the dependent variable Y. ,

Y measured value _{y k (k = 1,2, ···} , nn: number of measurements) and the predicted value given by Equation 5 from the measured values of the _{X i Y k (k = 1,2} , ··· , nn: the number of measurement data) (residual error) is a method for obtaining a partial regression coefficient b _i that minimizes the sum of squares Q of e _k .

Further, the probability of the partial regression coefficient obtained by the multiple regression analysis is represented by a value such as a multiple correlation coefficient.

Equation 3, for estimating the mass m _i of each marker position independently by multiple regression analysis from Equation 4, with respect to one mass marker position, and the estimated value from equation 3, is estimated from equation 4 There are two values that exist. Ideally, the estimated value of Equation 3 and the estimated value of Equation 4 should match, but in practice, they do not match very much. Therefore, by comparing the square sum Q of the residual obtained by regression analysis of the multiple regression analysis and formula 4 of the formula 3, by employing the estimated value m _i obtained by the equation towards Q is small as the mass of the marker position That's fine. Also, it may be determined from which formula the estimated value _mi is adopted from an index such as a multiple correlation coefficient.

  Alternatively, if the weighted position of the floor reaction force meter can be measured only in the x-axis direction and the three-dimensional motion analyzer can measure only in the x-axis direction, the equation 4 is used. Even when the weighted position can be measured only in the y-axis direction and the three-dimensional motion analysis apparatus can measure only in the y-axis direction, the expression used due to the limitation of the measuring apparatus can be selected. Good.

とし、式４の残差を

としたときに、e_xkの二乗和とe_ykの二乗和Qが最小になるような偏回帰係数m_iを求めてもよい。

この場合は、一意にマーカー位置の質量m_iを推定することができる。 In addition, instead of performing multiple regression analysis on Formula 3 and Formula 4 independently, multiple regression analysis may be performed on Formula 3 and Formula 4 together.
That is, the residual of Equation 3 is

And the residual of equation 4

And when, may be determined partial regression coefficients m _i as square sum Q of squares sum and e _yk of e _xk is minimized.

In this case, it is possible to estimate the mass m _i of uniquely marker position.

ここでm’は測定する部位以外の被測定者の質量である。被測定者が十分静的であればF_zは、被測定者の体重により床を押す力の大きさと等しくなり一定のはずである。F_zは被測定者の体重により得られるので、例えば事前に測定した被測定者の体重の±1%を基準値として、F_zの値がその基準値よりも大きいもしくは小さい測定データに関しては、被測定者が十分静的でないとして、前記の重回帰分析に使用するデータから取り除くという操作をしてもよい。この操作により、より正確にマーカー位置の質量m_iを推定することができる。
特許請求の範囲に記載の「基準値」は、被測定者が十分静的でない場合の測定データを取り除くための、鉛直床反力F_zに対する任意の値を意味する。 Incidentally, the vertical ground reaction force F _z satisfy the following equation as long as the subject does not the acceleration motion.

Here, m ′ is the mass of the subject other than the part to be measured. If the measurement subject is sufficiently static, F _z should be equal to the magnitude of the force pushing the floor depending on the weight of the measurement subject. Since F _z is obtained from the body weight of the measured person, for example, with respect to measurement data in which the value of F _z is larger or smaller than the reference value with ± 1% of the weight of the measured person measured in advance as the reference value, If the person to be measured is not sufficiently static, an operation of removing the data from the data used for the multiple regression analysis may be performed. This operation can be estimated mass m _i of the marker position more accurately.
The “reference value” described in the claims means an arbitrary value for the vertical floor reaction force F _z for removing measurement data when the measurement subject is not sufficiently static.

となる。ここで、x’、y’は測定する部位以外の被測定者の質量m’の前記任意の点からの距離である。被測定者は測定する部位のみ動かし、測定する部位以外の部分は動かさない。つまり、x’、y’は一定のはずである。したがってm’x’、m’y’を式５におけるb₀として式１２および式１３を用いて重回帰分析をすれば、マーカー位置の質量m_iを推定することができる。 In the present embodiment, M _x, but the moment exerted by the entire body of the subject around the reference point M _y, alternatively, M _x, a M _y of the subject around an arbitrary point It may be a moment applied by the whole body. For this arbitrary point, for example, the origin of a three-dimensional coordinate set at the corner of the floor reaction force meter can be used.
In this case, the terms of the mass m ′ of the person other than the part to be measured appear in the expressions 3 and 4,

It becomes. Here, x ′ and y ′ are the distances from the arbitrary point of the mass m ′ of the measurement subject other than the part to be measured. The subject moves only the part to be measured and does not move the part other than the part to be measured. That is, x ′ and y ′ should be constant. Therefore M'X ', M'y' if the multiple regression analysis using the equation 12 and equation 13 as b ₀ in Equation 5, it is possible to estimate the mass m _i of the marker position.

However, in this case, the number of partial regression coefficients is increased by one as compared with Equations 3 and 4, so that the accuracy of the multiple regression analysis may be deteriorated. In this regard, by the M _x, moment about a reference point M _y, wherein 3 to erase the term of b ₀ in Equation 5, it finds that using the equation 4 is preferred.

として、m’の影響を排除した式を用いて重回帰分析を行ってもよい。式１４、式１５では式３、式４と同様にb₀に相当する項が消去されるので偏回帰係数の数を少なくすることができ、重回帰分析に好適である。 Alternatively, since m′x ′ and m′y ′ are constant, Equation 12 and Equation 13 are differentiated with respect to time,

As described above, multiple regression analysis may be performed using an expression that excludes the influence of m ′. In Equations 14 and 15, the term corresponding to b ₀ is eliminated as in Equations 3 and 4, so the number of partial regression coefficients can be reduced, which is suitable for multiple regression analysis.

  In addition, Formula 14 and Formula 15 are suitable also when the value directly measured with a load sensor or a three-dimensional position measuring device is differentiated with respect to time. This is because multiple regression analysis can be performed without the need to integrate those measured values.

  The above formula 3, formula 4, formula 12, formula 13, formula 14, and formula 15 should just select the formula suitable by various measurement conditions, such as a measuring apparatus used for measurement.

[Step 4: Estimating the mass of the part]
Next, the mass m of the part to which the marker is attached is obtained from the estimated mass m _{i of the} marker position. Mass m of the site is determined by the sum of the mass m _i of the marker position.

x_i、y_i、z_iは３次元動作解析装置で測定した値を用いてもよいし、被測定者の部位を基準としてマーカーを取り付けた位置を別途測定した値を用いてもよい。 [5th step: Estimating the center of gravity of the part]
Then, from the mass m _i and the marker position of the marker positions, the center of gravity x _g at that site, y _g,, determine the z _g. The center of gravity is given by

For x _i , y _i , and z _i , values measured by a three-dimensional motion analysis apparatus may be used, or values obtained by separately measuring the position where the marker is attached with reference to the measurement subject's site may be used.

With the above procedure, the mass and the center of gravity of one part can be measured. Since the mass and the center of gravity of the measurement subject's part can be directly measured, the mass and the center of gravity of each part for each individual can be accurately measured without relying on statistical data.
Further, in the measurement of only one part, the measuring device becomes simple, and the mass and the center of gravity can be easily obtained from the measurement data.
In order to measure the mass of another part, it can also measure by changing a marker and repeating the above method.

(Measurement method for multiple parts)
Next, a method for simultaneously measuring the mass and the center of gravity of a plurality of parts will be described.

[First step marker setting]
First, a marker for a three-dimensional motion analysis apparatus is attached to a plurality of parts of the measurement subject. It is possible to attach markers to all parts of the subject's body and measure all parts at the same time, but if the number of markers is large, the accuracy of measuring the mass of the marker position will drop, so the upper arm and forearm, It is preferable to limit the region such as the thigh and the lower leg. The method of attaching the marker at each site is the same as that described above.

[2nd step: Measurement of marker position and moment]
As in the previous method, the person to be measured gets on the floor reaction force meter and slowly moves only the part where the marker is attached so that the acceleration is sufficiently smaller than the gravitational acceleration, and at the same time, the marker position is moved in three dimensions. The floor reaction force is measured with a floor reaction force meter using an analyzer. The measurement data of the marker position and floor reaction force are collected intermittently while changing the posture of the part.

ここでjはマーカーを取り付けた部位の番号であり、Mか所の部位にマーカーを取り付けた場合、j=1,2,・・・,Mである。すなわち、m_jiはj番目部位のi番目のマーカー位置の質量を意味し、x_ji、y_jiはj番目部位のi番目マーカーの基準姿勢からのx方向の変位およびy方向の変位を意味する。式２０、式２１を用いて前述と同様の方法で重回帰分析を行うことにより、各マーカー位置の質量m_jiを推定することができる。 [Third step: Estimating the mass of the marker position]
Next, the mass at each marker position is estimated from the collected measurement data.
Since markers are attached to a plurality of sites, the following equations are used instead of the above equations 3 and 4.

Here, j is the number of the part to which the marker is attached, and j = 1, 2,..., M when the marker is attached to the M part. That is, m _ji means the mass of the i-th marker position of the j-th part, and x _ji and y _ji mean the displacement in the x direction and the displacement in the y direction from the reference posture of the i-th marker of the j-th part. . By performing multiple regression analysis using Equation 20 and Equation 21 in the same manner as described above, the mass m _ji at each marker position can be estimated.

Of course, it is also possible to estimate the mass m _ji of each marker position by converting Equations 12, 13, 14, and 15 in the same manner and performing multiple regression analysis using the equations.

となる。式２２は以下のように変形できるので、

式２３を式２０、式２１に代入して

とすることができる。すなわち、m_MNを消去することで偏回帰係数m_jiを１つ少なくすることができ、重回帰分析の精度を向上させることができるのである。
式２４、式２５を用いて重回帰分析を行った後、m_MN以外の質量の推定値m_jiを用いて式２３からm_MNを求めることができる。 In addition, when attaching the markers for the three-dimensional motion analysis device to all the parts of the subject, the mass m ′ of the subject other than the part to be measured is lost in Equation 11,

It becomes. Since Equation 22 can be transformed as follows:

Substituting Equation 23 into Equation 20 and Equation 21

It can be. That is, it is possible to reduce one partial regression coefficients m _ji by erasing m _MN, it is possible to improve the accuracy of the multiple regression analysis.
After performing multiple regression analysis using Expression 24 and Expression 25, m _MN can be obtained from Expression 23 using an estimated mass m _ji other than m _MN .

[4th, 5th steps Estimation of the mass and center of gravity of the part]
From the mass m _ji of each marker position estimated using Equation 20, Equation 21 or Equation 24, Equation 25, the mass and the center of gravity of each part are obtained. Since the method is the same as described above, description thereof is omitted.

With the above procedure, the mass and the center of gravity of a plurality of parts can be measured simultaneously. Since the mass and the center of gravity of the measurement subject's part can be directly measured, the mass and the center of gravity of each part for each individual can be accurately measured without relying on statistical data.
In addition, since the mass and the center of gravity of a plurality of parts can be measured simultaneously, the mass and the center of gravity of many parts can be obtained in a short time.

(Other measuring devices)
In the above embodiment, the floor reaction force meter is used as the load sensor, and the three-dimensional motion analysis device is used as the three-dimensional position measurement device. However, an alternative device may be used.
As the three-dimensional position measuring device, for example, a goniometer is attached to each joint of the measurement subject, the angle of the joint is measured, and the length of each part of the measurement subject measured in advance and the length of each part of the measurement target 3. The dimension position may be obtained by calculation. In this case, it is necessary to measure the length of each part from the foot in contact with the floor to the part where the mass or the like is measured, and the angle of each joint.
Alternatively, the person to be measured may wear a sensor in which a gyroscope, an accelerometer, and a geomagnetic sensor are combined, and the three-dimensional position with reference to the earth may be obtained from the measured value.
In any of the three-dimensional position measurement apparatuses, the measurement method according to the present invention is the same except for the three-dimensional position measurement method.

The method for measuring the mass and the center of gravity of each part of the human body according to the present invention is used in the medical field, the sports kinematics field, and the like. For example, the mass and the center of gravity for each part obtained by the measurement method of the present invention are used as parameters when obtaining joint moments for each individual, and by extension, the muscle tension for each individual is estimated using a musculoskeletal model. Used for
In addition, the simulation of movement by modeling the human body is performed in various fields. The mass and the center of gravity obtained by the measurement method of the present invention are parameters for simulating movement for each individual. Also used as

Claims (10)

A first step of setting a measurement point on the assumption that the mass of the part is concentrated on the part of the subject;
Displacement x _i from the reference posture of the measurement point (i indicates the number of the measurement point);
The moment M applied by the entire body of the subject around any point,
A second step of measuring intermittently while changing the posture of only the part where the measurement point is set;
M / g = Σm _i x _i + m'x '
(G is gravitational acceleration, m _i is the mass of the measurement point, m ′ is the mass of the subject other than the measurement point, x ′ is the distance from the arbitrary point of the center of gravity of m ′, and Σ is the sum of the measurement points Show.)
Heavy using equation from data obtained by the second step, the mass m _i at the measuring point of the site, which dependent variable M / g, independent variable x _i, the m _i and the partial regression variables A third step of estimating by regression analysis;
A fourth step of obtaining the mass of said portion from the sum of the mass m _i of the measurement point,
A method for measuring the mass and the center of gravity of each part of a human body, wherein the fifth step of obtaining the center of gravity of the part from the mass _mi and the position of the measurement point is sequentially performed. In the first step,
2. The method of measuring mass and center of gravity of each part of a human body according to claim 1, wherein two measurement points are set for one part. In the first step,
3. The method of measuring mass and center of gravity for each part of a human body according to claim 1, wherein three measurement points are set for one part. In the first step,
The method of measuring mass and center of gravity for each part of a human body according to claim 1, wherein four or more measurement points are set so as not to be on the same plane for one part. In the first step,
2. The method of measuring mass and center of gravity for each part of a human body according to claim 1, wherein the measurement points are set only for one part. In the first step,
2. The method of measuring mass and center of gravity of each part of a human body according to claim 1, wherein measurement points are set at a plurality of parts. In the second step,
Measure the vertical floor reaction force,
In the third step,
The method according to claim 1, wherein when the vertical floor reaction force is larger or smaller than a reference value, it is removed from data used for multiple regression analysis. In the second step,
The moment M is defined as the moment applied by the entire body of the subject around the reference point, with the position of the center of gravity of the floor reaction force of the subject in the reference posture as the reference point,
In the third step,
M / g = Σm _i x _i
Of using a formula according to claim 1 body part by mass and center of gravity measurement method of wherein the estimating the mass m _i at the measuring point of the site. In the third step,
(dM / dt) / g = Σm _i (dx _i / dt)
(DM / dt is the time derivative of moment M, and dx _i / dt is the time derivative of displacement x _i .)
Of using a formula according to claim 1 body part by mass and center of gravity measurement method of wherein the estimating the mass m _i at the measuring point of the site. In the first step,
Set the measurement points on all parts of the subject,
In the third step
_{M / g = Σm i x i} + (F z -Σm i) x N
(F _Z is the vertical floor reaction force, N is the number of measurement points, and Σ is the sum of measurement points other than the Nth measurement point.)
Of using a formula according to claim 1 body part by mass and center of gravity measurement method of wherein the estimating the mass m _i at the measuring point of the site.

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