Optimization of the forearm angle for arm wrestling using multi-camera stereo digital image correlation: A preliminary study

Zixing Tong , Xinxing Sho , , Zhenning Chen , Xioyun He

a Department of Engineering Mechanics, School of Civil Engineering, Southeast University, Nanjing 211189, China

b College of Aerospace Engineering, Nanjing University of Aeronautics & Astronautics, Nanjing 210016, China

Keywords: Arm wrestling Skin deformation measurement Multi-camera stereo digital image correlation Close-range photogrammetry Forearm angle

ABSTRACT This study analyzes the function of different muscles during arm wrestling and proposes a method to analyze the optimal forearm angle for professional arm wrestlers.We built a professional arm-wrestling platform to measure the shape and deformation of the skin at the biceps brachii of a volunteer in vivo during arm wrestling.We observed the banding phenomenon of arm skin strain during muscle contrac- tion and developed a model to evaluate the moment provided by the biceps brachii.According to this model, the strain field of the area of interest on the skin was measured, and the forearm angles most favorable and unfavorable to the work of the biceps brachii were analyzed.This study demonstrates the considerable potential of applying DIC and its extension method to the in vivo measurement of human skin and facilitates the use of the in vivo measurement of skin deformation in various sports in the fu- ture.

Arm wrestling has been a popular sport since the 1950s, and there have been regional and international competitions.Most cur- rent studies on arm wrestling focus on bone injuries and robotics.The studies on the former topic mainly focus on injuries and their mechanisms during arm wrestling.For example, Maeder et al.[1] described a 24-year-old patient who sustained severe pain in the right arm during arm wrestling in 2017.The studies on the lat- ter topic mainly focus on the creation of wrist-wrenching robots that can imitate human athletes.For example, He et al.[2] de- signed an arm-wrestling robot system that can mimic the actual force-applying process of a human player in 2009.In addition, two studies on the sport of arm wrestling were conducted.Podri- halo et al.[3] divided experienced and less experienced athletes into two groups for grip strength testing, used the bioimpedance method to measure their muscle content, and observed that ath- letes with higher muscle content have a greater advantage.Podri- galo et al.[4] proposed a method for the prognostication of arm- wrestling success using morphological and functional indicators and observed that different postures of arm wrestling affect the outcome.However, they did not determine the posture that was most beneficial to arm-wrestling athletes.It is important to study the factors affecting the success of professional arm wrestlers.

For an arm-wrestling athlete, his opponent’s pulling force dur- ing arm wrestling has two components: one to extend the elbow, and the other to rotate the shoulder.The main muscles that re- sist elbow extension are the biceps brachii and brachioradialis, of which the former plays a major role.The main muscles that resist the external rotation of the shoulder are the pectoralis major, an- terior deltoid, and latissimus dorsi [5] .Since the biceps brachii and pectoralis major have little contact, we assume that the muscles that resist elbow extension and the muscles that resist external ro- tation of the shoulder work independently.This study focuses on the best posture to resist elbow bending (the forearm angle in this study).Therefore, the greater the moment produced against elbow extension, the greater is the probability of winning the competi- tion.More importantly, the moment is determined by the contrac- tion force and the moment arm of the biceps.The contraction force of the biceps can be reflected by measuring the strain of the skin at the biceps, and the moment arm can be calculated using the skeletal muscle model.However, skin deformation and muscle de- formation are not simple linear relationships; therefore, skin defor- mation in some places may be caused by several factors, such as body fat percentage, water content, collagen content, and muscle development [6] .For simplicity, the target of our measurement is the skin strain at the belly of the biceps brachii, as the strain at this location has the strongest correlation with the deformation of the biceps brachii.

Several optical methods, such as digital moiréinterferometry (DMI) [7] , laser speckle imaging (LSI) [8] , fringe projection (FP) [9] , and digital image correlation (DIC) [10] , can be used to measure the deformation and shape of human skin.The above methods facilitate noncontact, full-field measurement, but they have some disadvantages.For example, for DMI, the correlation between the laser speckle and interferometry decreases with time.The speck- les produced by LSI are uncontrollable, and their accuracy depends on the roughness of the surface.Although FP is a powerful optical method, it is not suitable for deformation measurements.In con- trast, the DIC method is ideal for the in vivo measurement of hu- man skin.In addition to the in vivo measurement of human skin, there are also some in vivo measurements of animal skin for bion- ics.For example, in order to study the adsorption and deforma- tion mechanism of leech, Li et al.[ 11 ] used a high-speed camera to measure the skin of the leech in vivo.However, the strain of the skin was given by a testing machine rather than an optical mea- surement method.They used the camera only to observe the ap- pearance of the leech in the experiment.

The stereo-DIC and multi-camera DIC (MC-DIC), which were developed based on the conventional DIC and stereo vision can be used to measure three-dimensional (3D) deformation of planar and curved objects.These methods have been widely used for the in vivo measurement of human skin.For example, Khatam et al.[12] measured the deformation of female breast skin, Chen et al.[13] measured the deformation of female facial skin, and Chen et al.[14] measured the deformation of the skin of the human carotid artery.The MC-DIC method is used in this study, and the specific principle of the technique is introduced in the following section.

The stereo-DIC method has been widely used in industrial mea- surement and has several precedents in the in vivo measurement of the deformation of human skin [12-14].A schematic of stereo- DIC is shown in Fig.1 .For each world pointPW, the world co- ordinates(X,Y,Z)can be solved using their coordinates(x1,y1)and(x2,y2)in the left and right camera coordinate systems ac- cording to Eqs.(1) and (2) .The projection matrix of the left and right camerasMican be obtained by multiplying the intrinsic matrixAiand extrinsic matrixBi, wherefxiandfyiare the focal lengths,are the principal point coordinates,RiandTiare the rotation and translation matrices, respectively, andZciis the scale factor:

The 3D displacement field can be obtained by subtracting the 3D coordinates of the point at two moments, and the 3D strain field can then be obtained using the least-squares fitting method.

As there are several complex parts of the human body, panoramic measurement using only two cameras is not possible; therefore, multiple (more than two) cameras need to be used for the measurement [15–17] .The current multi-camera DIC methods can be divided into two categories: a method that requires cam- eras to have overlapping fields of view (FOVs) [18] and a method that does not [19] .

Figure 2 shows the workflow of the MC-DIC used in this study.Step 1 involves the reconstruction of a marker using a single cam- era, including pasting encoded targets on the marker, close-range photogrammetry, and 3D reconstruction.Step 2 aims to calibrate the four cameras and the two stereo-DIC systems.In step 3, as the 3D information of the marker is known, the coordinate transforma- tion matrix between the two subsystems can be obtained.In step 4, the speckled (on the volunteer’s arm) images are captured by the two stereo-DIC systems, which can calculate each half of the 3D strain field and then splice them together.

A professional arm-wrestling table and height-adjustable chairs were used in this study to simulate a natural arm-wrestling envi- ronment.Figure 3 a shows the overall experimental scene, includ- ing an arm-wrestling table, height-adjustable chair, computer, and multi-camera stereo DIC (MC-DIC) system composed of four cam- eras connected to a computer.Four synchronized 2048 pixel ×2048 pixel IDS cameras (UI-1540LE-M-GL) equipped with four 16 mm Kowa lenses were arranged on two tripods beside the table.The MC-DIC system has two subsystems: camera pair 1 on the left and camera pair 2 on the right.The two subsystems shoot contes- tants from the left and right, and finally fuse the captured images into 3D images.Figure 3 b shows a top view of the arm-wrestling table, where A is the elbow mat for the contestants, B is the mat that judges the outcome by contact, and C is the grip for the other hand.The height-adjustable chair is shown in Fig.3 c.

Initially, as a carrier of deformation information, the water- transfer-printed speckle patterns [13] were pasted onto the area of interest (AOI)—the skin at the biceps brachii of contestant 1.To ex- plore the impact of different forearm angles on arm wrestling, first, the white tape was pasted along the diagonal of mat A (Fig.3 b) to determine the center of the mat, and contestants were required to place their elbows at the center of the mats in each experi- ment.As shown in Fig.4 a, as the distance between the elbows and the length of the contestant’s forearm were constant, the triangle ABC was always uniquely determined.Therefore, we could adjust the height of the seat to change the height of the shoulders.With other conditions unchanged, we can consider that the higher the position of the shoulder, the smaller the angle of the forearm.Ac- cording to the height of the chair, the forearm angle was divided into five angles, from acute to obtuse.As the height of the chair and table, upper body length, and upper arm length of the con- testant can be measured, the precise forearm angleαican be ob- tained from the triangle relationship (Fig.4 b) as follows:

whereαiis the forearm angle,βis the constant angle between the forearm and the table,LF1,2 is the length of the forearm of contes- tants 1 and 2,LMis the distance between the centers of the two mats,LU is the length of the upper arm,LBis the height of the up- per body,LCiis the height of the chair, andLE is the height from the ground to the elbow.

Contestant 1 performed arm wrestling with the more robust contestant 2 at five different angles (Fig.5).As the more robust contestant 2 exerted force to maintain the wrist in a neutral po- sition, contestant 1 gradually exerted pressure until it reached the maximum.The skin deformation at the biceps brachii of contestant 1 was recorded using the MC-DIC system during this process.The experiment was repeated three times at each angle, and the con- testants rested for 10 min between each experiment to ensure that they had sufficient time to recover.The experiment was conducted in an ethical manner.

Using the stereo-DIC software of the research group, we mea- sured the 3D topography and strain field of the skin under each stereo-DIC system.Then, 3D information can be converted to the same stereo-DIC coordinate system according to the coordinate transformation matrix between different stereo-DIC systems.Thus, 3D splicing is completed.

Figure 6 a and 6 b shows the 3D strain fields obtained using camera pairs 1 and 2, respectively.The spliced 3D strain field is shown in Fig.6 c, where the red positive strain area corresponds to area A in Fig.6 d, and the blue and green negative strain areas correspond to area B in Fig.6 d.

In Fig.6 d, area A is the muscle belly, and area B is the tendon.When the contestant exerts a force, the biceps brachii contracts—muscle fibers gather toward the muscle belly, which causes the skin at the muscle belly to tighten and the skin at the tendon area to relax.Therefore, the strain of the skin at the muscle belly is positive, and the strain of the skin at the tendon area is negative.

Based on the images captured from the internal subsystem, we can easily observe the contour of the skin at the biceps brachii belly through the purple dividing line, which illustrates that the skin at the edge of the biceps is hardly stretched.However, the skin above and below the dividing line has considerable deforma- tion due to muscle contraction, and the strain of the skin above the dividing line is in a distinct band (Fig.7), which can be considered as the AOI.We observed that the slight difference in the selec- tion of the banded area had little effect on the average strain of this area.Therefore, in each experiment, the banded area was arti- ficially selected, and the curve of the average first principal strain of the AOI over time was recorded.Moreover, its peak value was regarded as an index representing the degree of muscle contrac- tion at that angle.

Thus, we obtained the index of the degree of muscle contrac- tion.The next step is to obtain the moment arm.For elbow move- ment, the axis of rotation is the elbow joint.According to the structure diagram of the human arm (Fig.8 a), the biceps brachii starts from the scapula and ends at the radius.The arm can be simplified to the mechanism shown in Fig.8 b, where A and B are the starting and ending points of the biceps brachii, respectively, C is the elbow joint,αis the forearm angle,l1 is the distance from the ending point B to the elbow joint C,l2 is the length of the humerus (≈LU), andl3 is the moment arm.l3 can be calculated using Eq.(5) , wherel1 ≈3 cm .Therefore,Rcan be used as the in- dex of the moment, obtained by multiplying the index of the con- traction force (skin strain) and arml3.The larger the value ofR, the stronger is the ability to resist elbow bending.

Table 1 presents some constant lengths in Fig.4 b.Table 2 presents the chair heights at different angles, forearm angles, and the peak value of the average first principal strain of AOI.

Table 1 List of values of constant lengths.

According to the data in Table 2 , Fig.9 shows the fitting curve ofl3 -angle and contraction force-angle fitting curve.We can see that as the angle increases, the moment arm first increases and then decreases, while the contraction force first decreases and then increases (although it decreases afterwards).By multiplying the moment arm and the contraction force, we can get theR-angle fit- ting curve.Figure 10 a shows theR-angle curve fitted with a fourth- order polynomial.For contestant 1, 105 °–110 °and 72 °–78 °are the ranges of the most favorable forearm angles, and 85 °–95 °is the range of the most unfavorable forearm angles.When the volun- teer competes at the best angle, his biceps brachii will provide the maximum moment to help him win the game.Several professional arm wrestlers choose smaller or larger forearm angles to compete, as shown in Fig.10 b.Angles less than 72 °are difficult to achieve in actual experiments and violate the physiological structure of the contestants; therefore, no experiment was performed at these an- gles.Notably, the best angle obtained in this study is relevant only for this volunteer and does not apply to others.In addition, the angle in this study was measured under the standard proposed; hence, the value may deviate from the angle under intuitive per- ception.

Table 2 Various parameters at different angles.

This paper describes in detail the principle and process of us- ing MC-DIC to measure the deformation of human arm skin.Us- ing the MC-DIC method, we observed the banding phenomenon of arm skin strain during muscle contraction and obtained the 3D profile and strain field of the skin at the biceps brachii during arm wrestling.According to the experiment, we obtained the best and worst angle ranges for the participant’s biceps brachii dur- ing arm wrestling.We observed that 72 °–78 °and 105 °–110 °are the preferred forearm angle ranges for this participant.This study can guide professional arm-wrestling athletes and training teams.Moreover, it confirms that it is feasible to use MC-DIC to measure the deformation of human skin in vivo and obtain a 3D profile and surface strain.This method can be used in future research on com- petitive sports.

Data availability

The data that support the findings of this study are available from the corresponding author upon reasonable request.

Disclosures

The authors declare no conflicts of interest.

Declaration of Competing Interest

The authors declare that they have no known competing finan- cial interests or personal relationships that could have appeared to influence the work reported in this paper.

Acknowledgments

This study was supported by the National Natural Science Foun- dation of China (NSFC) (No.11902074).