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This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution license (http://creativecommons.org/licenses/by/3.0/).

The paper presents a multifunctional joint sensor with measurement adaptability for biological engineering applications, such as gait analysis, gesture recognition,

Measurement of human pose and motion generates interest among researchers because of their wide applications in fields such as gait analysis [

Inertial measurement units (IMUs), compact wearable devices that contain a triaxial accelerometer and a triaxial gyroscope, are some of the most popular devices used to sense movement and orientation of the moving body that can help calculate joint angles because of their capability of reconstructing the trajectory of sensed anatomical points. Kinematic values such as shank and thigh inclination angles, knee joint angles or elbow joint angles can be derived by integration of angular acceleration or angular velocity [

Vision-based systems are another popular method for tracking motion and recognizing the pose of humans. Single or multiple cameras acquire video streams that are processed and gestures are mapped into temporal signatures of changes in video frames [

Additionally, methods for joint angle measurement based on other principles were also proposed. The main problem of the bio-measurement method [

This study aims to develop a joint angle sensor with measurement adaptability. The adaptability is embodied in suiting both static and dynamic environment measurements, both pose and motion capture, and the capability of simultaneously measuring MDOF with a single sensor to reduce system complexity. It is preferable for the sensor to be flexible for measurement of multi-axial joints, such as shoulders, ankles,

Capability of measuring 3DOF simultaneously with two working modes. The basic mode works for achieving orientation and obliquity of a three-dimensional (3D) joint. The optional advanced mode is able to measure an additional DOF.

The basic mode enables the applications on different joints of different individuals without recalibration.

Large ranges of measurement for freely arbitrary movement. The orientation is over the range 360°. The ranges of obliquity and additional angle can be designed by requirement.

Pose and motion capture in both static and dynamic environments.

Utilization of the minimum number of outputs for reconstructing three angular parameters. This will greatly reduce the volume of testing data compared to other approaches. The simple reconstruction algorithm and small data volume are capable of providing real-time angles and long-term monitoring.

Other characteristics such as flexibility and insensitivity to environment disturbances.

Skin is an organ of the integumentary system that protects the underlying muscles and organs. It is flexible and has many wrinkles, especially on the joints. Movement of extremities cause the corresponding extension/accumulation of wrinkles. If we draw several black lines on the elbow, their length will differ with different joint motions, thus the angular parameters are converted into length changes, but it is difficult to measure the actual length of skin and it differs between individuals. A corrugated tube shaped into alternating parallel grooves and ridges is selected as the sensor body to imitate the action of skin, as illustrated in

Two important characteristics of the tube are keeping the constant radius of the ridges and resisting twisting. The tube ends are mounted on the two segments of the tested object, whose relative position indicates the 3D joint spatial status.

The multi-axial joints of the human body are mainly the wrist, shoulder, hip and ankle. Two angular parameters can describe their spatial relative position. Among them, the shoulder and hip joints can be similar sketched as ball and socket joints with three DOF. Generally, the Euler angles are three angles introduced by Euler to describe the orientation of a rigid body. They are the azimuth

According to _{1}_{1}_{2}_{2}_{3}_{3}_{x}) is the bending central point of the tube central axis with the obliquity as _{x}. _{1}, _{2} and _{3} represent the length of _{1}_{1}_{2}_{2}_{3}_{3}_{1,2,3}(_{x}) are the bending radius of three lines that are parallel to

They are the functions of orientation _{x}) is the bending radius of the tube central axis that changes gradually with obliquity, and

Substituting _{1}, _{2} and _{3} are expressed as:

The subtraction of each two equations will eliminate the integral part. _{1}, _{2} and _{3} and radius

Based on the introduced principle, a sensor capable of measuring the surface lengths of corrugated tube is proposed. A prototype is built to test the feasibility of the method. Its configuration is shown in

The sensing element prototype is built to test the wire displacement, which is mainly composed of a stainless wire, a 10-turn rotary potentiometer and a DC motor, as shown in

Wires of three sensing elements run through the tracks built on the flexible tube, respectively. Their free ends are fixed on the tube by ring 1 and then clustered into one bundle by the small hole on ring 2. The design of ring 1 and ring 2 is used to induce the optional advanced working mode. The end of the flexible tube and three testing segments are mounted in a case as shown in

Movement of the wire leads to the rolling of the potentiometer to represent a voltage divider. Three DC voltages _{1}, _{2} and _{3} are measured as outputs by a digital multimeter (DMM). Three motors used to roll back the potentiometers are driven by a DC voltage source of 2 V which is able to control the strain on the wires. In order to achieve the characteristics and prove the feasibility of the proposed sensor structure, an experimental platform is built, which is a mechanical frame imitating a joint with two freedoms of motion, containing orientation scale and obliquity scale. Two ends of the prototype are fixed on the frame upper side and under side. By accurately adjusting the relative position of two ends of the frames with scales, the prototype can be set to the required positions with orientation

The purpose of fabricating the prototype is only for proving the feasibility of the proposed method. The basic configuration and working principle of proposed sensor are more meaningful than the detailed structure of prototype. The size of the actual device can be designed freely depending on the tested object. The tube radius is the most important and the only required parameter for the subsequent estimation process.

The device outputs can be expressed as _{1,2,3}= _{0}+ Δ_{1,2,3}, where _{0} is the output at initial position and Δ_{1,2,3} are the variations of _{1,2,3}. The relations of three voltages and displacement of wires is expressed as below:
_{v} is the voltage change with 1 mm displacement of wire which is a constant only decided by the potentiometer and its shaft size. We suppose _{1,2,3} = _{0} + Δ_{1,2,3}, where _{0} is the length of wires at initial position, and Δ_{1,2,3} are the displacements separately. From _{v} and

Besides the measurement of

In the basic mode,

Generally, three uncorrelated equations have the capability to calculate three unknown variables. The attachment of sensor on different individuals produces different expressions

The subtraction between each two equations of

In the basic mode, the ends of wires are fixed on the end of the tube by ring 1. In the advanced mode, ring 1 is loosened and the bundle composed of three wires is able to move through the hole on ring 2. The end of the bundle is fixed on the segment of an additional joint, the pose of which is described by

Measurement of an additional uniaxial joint angle

The application contains two aspects. One is the addition of a traditional uniaxial joint, such as adding a knee angle to an ankle joint measurement or adding the rotation angle of forearm (pivot joint) to the wrist joint. The other one is the additional measurement of another DOF of a joint with 3DOF motion, such as the rotation of a shoulder and hip joint. For the shoulder joint, the rotation angle is led by the rotator cuff muscles attached on the proximal humerus and is a gradual change from the shoulder joint to the elbow. The mounting of tube end on the area of deltoid muscle efficiently reduces the effect caused by rotation. The bundle end is fixed on near the elbow to test the shoulder rotation. Two examples are illustrated in

Extension for the measurement of an additional 2DOF joint

The main purpose of the advanced mode lies in reducing the number of sensors mounted on human joints. Besides the measurement of an additional uniaxial joint, the combination of several sensors can realize interesting applications, such as the additional measurements of the waist by employing two advanced mode hip sensors. _{w} and _{w} are used to describe the relative position the ribcage and hips. Two hip sensors are placed on the outboard of the femur and the pelvis, which have a 180° phase different in waist orientation. Γ(_{w}, _{w}) and Γ(_{w} + π, _{w}) for the two sensors. With the calculated value of Γ(_{w}, _{w}) and Γ(_{w} + π, _{w}), the _{w} and _{w} of waist can be reconstructed.

In _{v}. _{v} is the voltage change with 1 mm displacement of wire and _{v} is calculated by least squares fitting on the experimental results instead of using the product data. Δ_{1,2,3} are measured with the displacement _{v1} = 8.361 mV/mm, _{v2} = 8.429 mV/mm and _{v3} = 8.404 mV/mm, respectively, with a linear tolerance of 0.38%. _{v} is their average value for a simple data process, which is 8.4 mV/mm.

Experimental results on sample positions are employed to reconstruct angular parameters and analyze the characteristics of proposed sensor. Sample positions are set with _{1}, _{2} and _{3} on each sample position are measured in sequence by DMM.

In _{1} − Δ_{2} and Δ_{1} − Δ_{3} with

The curves are sinusoidal and their magnitudes depend on the value of obliquity. The phase difference of Δ_{1} − Δ_{2} and Δ_{1} − Δ_{3} is the angular separation of wires. _{1} − Δ_{2} and Δ_{1} − Δ_{3} with

This is a ternary function reconstruction problem because each sensing element is cross- sensitive to three angular variables. The process flow of angular parameter reconstruction is shown in

Orientation can be calculated by dividing each equation of _{1} − Δ_{2})/(Δ_{1} − Δ_{3}) and

From

In

The forearm, arm or thigh can be sketched as elliptic cylinders. _{1}, Δ_{2} and Δ_{3} are measured with

In

The expression of Γ(_{c}_{c}

For the reason that the twisting experiment is done with _{1,2,3} are generated only by a single variable _{1,2,3}. In a practical application, fitting the equation of Γ^{−1}(

The inaccuracy of the prototype in basic mode is approximately RMSE = 1.01° in orientation, and RMSE = 1.22° in obliquity. The inaccuracy of the third angle changes with different working situations.

In the basic mode, the hysteresis of the tube has little effect on the estimated results because of the elimination of the integral part. Therefore, the dynamic character of the proposed device mainly depends on the sensing element used for the displacement measurement. The wire acceleration of some commercial wire-type displacement sensors reaches 10 g. The device is able to measure the high speed motion such as that of athletes by employing a high level linear displacement sensor. The direct and immediate measurement of joint angles can help calculate the velocity and the acceleration during the movement.

The measurement of orientation is full range, while the range of obliquity and the additional angle parameters can be increased freely by increasing the measurement range of the wire displacements. Use of a high level linear displacement sensor will increase the accuracy. As to practical applications, after determining the tube radius first, by considering the whole range of actual joint motion, the maximum displacement of each sensing element can be achieved by experimentation or calculation. Then we can choose the sensing elements with the corresponding range to build the device. The flexibility and big range of estimated angles is suitable for various applications.

The proposed device is simple but maybe still be somewhat cumbersome. Our future work will try to reduce its size for convenience. The soft tissues of the body may allow positioning of the sensor relative to the body to change as motion occurs. Therefore, a firm mount on human body and

The paper has proposed a multifunctional joint sensor with measurement adaptability for human gesture measurement. The sensor imitates the skin and utilizes a corrugated tube as the main body, which is flexible and contributes to the wearable character of the sensor with less restraints. Its multifunctional capability lies in its ability to simultaneously measure MDOF with a single sensor, which is designed in two working modes. The basic mode works for determining the orientation and obliquity of a 3D joint over big ranges and stands out for its applications to different joints of different individuals without recalibration. The optional advanced mode enables an additional DOF measurement to benefit a variety of applications. Although the advanced mode increases the algorithm complexity, it can reduce the physical system complexity. There are only three outputs of the proposed sensor, which is the minimum number needed for reconstructing three angular parameters. This will greatly reduce the volume of testing data compared to other approaches.

No use of inertial elements and the compact structure of the device provide the adaptability for both static and dynamic environment measurements, and both body pose and motion capture. The simple reconstruction algorithm and small output data volume are capable of providing real-time angles and long-term monitoring with environmental universality. The performance assessment of the built prototype is promising enough to indicate the feasibility of the sensor.

This research is supported by the China National Science Foundation Grant No. 61102038 and Grant No. 51138003. The author would like to thank Katsunori Shida, University of Saga, for the valuable suggestions.

The authors declare no conflict of interest.

Working principle and corrugated tube character.

Skeleton of shoulder joint and definitions of 2DOF.

Geometric analysis (

Configuration of the prototype. (

Advanced mode (_{w} and _{w} of waist by employing two hip sensors.

Experimental results on sample points.

Analysis of sensor outputs (_{1} − Δ_{2} and Δ_{1} − Δ_{3}: Sinusoidal relation with orientation; (_{1} − Δ_{2} and Δ_{1} − Δ_{3}: Linear relation with obliquity.

Process of three parameters reconstruction.

Estimated

A structure imitates the measurement of torsion angle of shoulder joint.

2D interpolation of

Estimation of torsion angle