various movements are possible in the human body because many segments are connected by 
 joints1 . then muscle tension occurs , and the total tension is known as 
 muscle strength3 . muscle strength is determined by the recruitment of a number of motor units3 , and muscle activation represents the degree 
 of activity of motor units4 , so muscle 
 strength is related to muscle activation5 . since muscle strength is affected by the change in length of the muscle when it contracts , 
 when we look at the length - tension curve of muscle , the largest amount of tension can be 
 seen within a specific range of muscle lengths6 . the change in muscle length hence , the change in joint angle affects muscle contractive force and its 
 function7 , 8 , and therefore joint angle can be a variable affecting the maximum 
 force that is generated by the muscle9,10,11 . most existing research has been about the relationship between maximum muscle strength and 
 the change in muscle length , and the existing reports contain conflicting results . gandevia 
 and mckenzie12 stated that muscle 
 activation is always constant regardless of the muscle length . meanwhile , nicholas et 
 al.13 stated that changes in muscle 
 length affects muscle activation . an et al.7 , kim14 , and 
 kim15 mentioned that the change in 
 joint angle and muscle length can be a variable to muscle activation and contractive 
 force . kasprisin and grabiner16 stated that the 
 shorter the muscle length , the higher the muscle activation , whereas komi et al.17 stated that decreases in muscle length 
 lower the muscle activation . generally , considering the length - tension curve of muscle , it 
 is known that changes in muscle length can affect muscle activation , but previous research 
 has reported various results about the relation between muscle length and strength . nevertheless , to minimize injuries when performing exercises for muscle strength in 
 different position for the purposes of rehabilitation and health promotion and to enable 
 performance of exercise comfortably18 , it 
 is vital to investigate optimal joint angle and muscle length . since it is important to 
 consider the exercise position or joint angle position that can accomplish the purpose of 
 the exercise from the planning stage19 , 
 it is necessary to investigate the optimal muscle length and joint angle for generation of 
 the maximum muscle strength20 . however , because the lengths of all muscles are different , it is difficult to objectify and 
 generalize a standard muscle length and conditions that produce the maximum muscle strength . hence , a research study regarding the relation between muscle angle ( which is comparatively 
 easier to objectify and generalize than muscle ) and muscle strength was undertaken . nam21 measured the muscle strength at elbow 
 flexion angle of 110 to 70 degree in 5-degree intervals , and na22 measured the muscle strength at hip joint angle of 90 to 
 160 degrees in his research . but these studies are only applicable to particular joints , so they could not provide 
 generalized standards for all joints . considering the length - tension curve of muscle in 
 particular , a scientific basis for the optimal joint angle that is objectively applicable to 
 all the joints has not been provided . therefore , the aim of this study was to find the best 
 way to generalize all the joints , taking into consideration the length - tension curve of 
 muscle . the participants in the present study were 15 male and 15 female students attending s 
 university in busan , republic of korea . the average age of the male students was 
 24.01.0  years , their average height was 173.06.1  cm , and their average weight was 
 70.08.2  kg . the average age of the female students was 23.00.0  years , their average height 
 was 159.05.4  cm , and their average weight was 54.05.3  kg . the purpose and methods of the 
 research were fully explained to the participants before the experiment was carried out . this study complied with the ethical standards of the declaration of helsinki , and written 
 informed consent was received from each participant . the participants were healthy students 
 who had no functional disability with respect to measuring muscle strength and muscle 
 activation , and none who had any experience of damage to an upper extremity or hand . the elbow joint was selected to examine the relation between range of motion and muscle 
 strength and activation . a professional goniometer set ( patterson medical , p.r . china ) was 
 used to measure the angles of the elbow joint of the participants . the line connecting the 
 greater tuberosity of the humerus and lateral epicondyle was set as the fixed axis of the 
 goniometer . the radial head of the forearm was set as the standard on the axis of rotation 
 of the goniometer . the resting position of the shoulder was adduction of 55 , whereas the 
 horizontal adduction was 30. the resting position of the elbow joint was elbow flexion of 
 70 and supination of 10. a sthenometer ( biodex system iii , biodex medical system , shirely , 
 usa ) was used to measure the muscle strength of the elbow during performance of isometric 
 exercise . the subjects were asked to sit on the measuring chair , and the condyle of the 
 humerus was adjusted to be perpendicular to the axis of rotation of the dynamometer . to 
 avoid using other parts of the body , straps were used to immobilize the chest and the lower 
 legs . muscle strength and activity were measured at the angles of 56 , 70 , and 84. after 
 each fixed angle was set , flexion and extension were carried out alternately through 
 isometric exercise , and the muscle strength was measured . according to sons18 research , the 
 maximum tension of the muscle is shown when the muscle length is more than 1.2 times longer 
 than at the resting point . hence , angles were selected that represented a 20% stretch 
 compared with the resting position of the elbow joint . flexion was performed with the biceps 
 stretch 20% at an angle of 56 , and extension was performed with the triceps stretched 20% 
 at an angle of 84. measurements were taken at 56 , 70 , and 84 accordingly . at each angle , 
 the isometric strength of flexion was measured . after a 10-second break , the isometric 
 strength of extension was measured . to prevent muscle fatigue , 3 minutes of rest measurements were performed 3 times , and the average of 
 the 3 measurements was used for analysis . to facilitate holding an accurate position while 
 the movements were performed , two practice trials were carried out before proceeding with 
 the main experiment . while muscle strength was being measured , surface electromyography ( keypoint , medtronic , 
 minneapolis , mn , usa ) was used to measure the muscle activation of the biceps brachii and 
 triceps brachii . a disposable surface electrode that was 1.2  cm to 2.5 cm long was used as 
 the electrode , and a unipolar surface electrode with a diameter of 3  cm was used as the 
 ground electrode . to decrease the effect of the resistance of the skin on the electromyogram 
 signal , all hair at the electrode attachment site was removed , and rubbing alcohol was used 
 to remove the skin oil before attaching the electrode . next , a small amount of electrolyte 
 jell was used to attach the electrode to skin . the electrodes were attached to the bellies 
 of two muscles ( biceps brachii muscle and triceps brachii muscle ) , and there was a 1  cm 
 space between the two electrodes . the emg values collected were the root mean square of each muscle s rms values for 4 
 seconds . the emg value for only the last 3 seconds was used for analysis ( thereby excluding 
 the first second ) . repeated measures anova was used to check if there was any difference in 
 muscle strength and muscle activation at the angles of 56 , 70 , and 84 in the statistical 
 analysis . the results of examining the difference in elbow joint angle and elbow joint muscle 
 strength are shown in table 1table 1 . the differences in muscle power according to angle ( unit : nm)variables567084maximum torqueflexion34.217.132.414.631.414.4extension*26.89.927.98.929.89.8mean torqueflexion*31.416.029.914.428.214.2extension*23.99.424.18.327.59.2meansd . * : repeated measures anova test ( p<0.05 ) . by paired t - test : 
 56>84 ( p<0.05 ) . 70<84 ( p<0.05 ) .. regarding flexion of the elbow joint , the maximum torque value were 34.2 nm 
 at 56 , 32.4 nm at 70 , and 31.4 nm at 84. the value was highest at 56 , but there was no 
 statistical difference . on the other hand , after examining the differences between the 
 angle , it was apparent that maximum torque value at 56 was higher than at 84 ( p<0.05 ) . 
 with extension of the elbow joint , the maximum torque values were 26.8 nm at 56 , 27.9 nm at 
 70 , and 29.8 nm at 84 , demonstrating a difference at each angle ( p<0.05 ) . after 
 examining the differences between the angle , it was found that the maximum torque value at 
 84 was higher than those at 56 ( p<0.05 ) and 70 ( p<0.05 ) . with flexion of the elbow 
 joint , the average torque value were 31.4 nm at 56 , 29.9 nm at 70 and 28.2 nm at 84 
 ( p<0.05 ) . after examining the difference between the angles , it was found that the 
 average torque at 56 was higher than that at 84 ( p<0.05 ) . with extension of the elbow 
 joint , the average torque values were 23.9 nm at 56 , 24.1 nm at 70 and 27.5 nm at 84 , 
 demonstrating a difference at each angle ( p<0.05 ) . after examining the difference between 
 the angle , it was found that the average torque at 84 was higher than those at 56 
 ( p<0.05 ) and 70 ( p<0.05 ) . * : repeated measures anova test ( p<0.05 ) . by paired t - test : 
 56>84 ( p<0.05 ) . 56<84 ( p<0.05 ) . the results of investigating the effect of elbow joint angle on muscle activation of the 
 biceps and triceps are shown in table 
 2table 2 . the differences in muscle activation according to angle ( unit :  mv)variables567084biceps activationflexion*617.7158.6555.5156.9503.3152.3extension*489.9140.0455.6150.7412.9137.4triceps activationflexion*370.0162.4420.4174.3489.9191.0extension*422.6192.7498.1215.7599.3234.5meansd . * : repeated measures anova test ( p<0.05 ) . by paired t - test : 
 56>70 ( p<0.05 ) . 70<84 ( p<0.05 ) .. the muscle activation levels of the biceps at the different angles of flexion 
 were 617.7  mv at 56 , 555.5  mv at 70 , and 503.3  mv at 84 , with significant differences 
 being found at each angle ( p<0.05 ) . the results showed that muscle activation at 56 was 
 greater than at 70 ( p<0.05 ) and at 84 ( p<0.05 ) and that muscle activation at 70 was 
 greater than at 84 ( p<0.05 ) . regarding extension , the muscle activation levels of the 
 biceps were 489.9  mv at 56 , 455.6  mv at 70 , and 412.9  mv at 84 , with significant 
 difference being found at each angle ( p<0.05 ) . the results showed that muscle activation 
 at 56 was higher than at 70 ( p<0.05 ) and at 84 ( p<0.05 ) , and that muscle activation 
 at 70 ( p<0.05 ) was higher than at 84 ( p<0.05 ) . the muscle activation of triceps 
 showed that at flexion it was 370.0mv at 56 , 420.4mv at 70 , and 489.9mv at 84 , which 
 showed a difference at each angle ( p<0.05 ) . the result of different angles showed that 
 muscle activation at 84 was higher than at 70 ( p<0.05 ) and at 56 ( p<0.05 ) , and 
 muscle activation at 70 was higher than at 56 ( p<0.05 ) . at extension , the muscle 
 activation levels of the triceps were 422.6  mv at 56 , 498.1  mv at 70 , and 599.3  mv at 84 , 
 with significant differences being found at each angle ( p<0.05 ) . the results showed that 
 muscle activation at 84 was higher than at 70 ( p<0.05 ) , and that at 56 ( p<0.05 ) , 
 and muscle activation at 70 was higher than at 56 ( p<0.05 ) . * : repeated measures anova test ( p<0.05 ) . by paired t - test : 
 56>70 ( p<0.05 ) . for each joint of the body , there exists an optimal advantageous joint angle2 , and at that angle , the muscle will have an 
 optimal length that can exert the maximum power23 . after all , muscle strength is determined by the length - tension 
 relationship of the muscle and the mechanical qualities of a lever . so it is important to 
 know the relationship between muscle strength and joint angle in order to carry out more 
 effective muscle strength improving exercise24 . in connection with this , lee25 stated 
 that when carrying out a movement , if the optimal muscle length and joint position are fixed 
 at the appropriate place , the maximum power can be generated comfortably , and the exercise 
 can be performed more effectively . in other words , because muscle strength is affected by 
 the joint angle , exercise should be performed at an angle at which the maximum muscle 
 contraction can take place to exert the largest force . however , the fact is that up to now 
 there has not been a scientific basis for the optimal joint angle that is objectively 
 applicable to all the joints . borstad26 stated that generally a 
 movement takes place at the resting position when the resting length of the muscle related 
 to the movement is shortened . so to find out the optimal joint angle , it is appropriate to 
 set the joint angle of the resting position as the standard . cooke and fay27 explained that although the active force 
 of a muscle is highest a muscle s resting length , when the muscle length is stretched 2030% 
 beyond the resting length , the passive force increases , and the total force also becomes 
 greater . hence , in this research , we chose to examine the relationship between joint angles 
 at which the muscle was stretched to 20% more than the resting position and muscle strength 
 in order to provide a scientific basis that is applicable to all the joints . first , when 
 selecting the joint angle of the elbow , the resting position and muscle length - tension 
 relationship were used to select 3 kind of joint angles . the angles of 56 and 84 were 
 selected because these two angles represented the angles at which the agonist biceps and 
 triceps were stretched 20% during concentric and eccentric contraction and were the angles 
 at which the maximum muscle strength was seen . the results of the present study showed that 
 muscle strength and muscle activation of the biceps were highest at the joint angle of 56 , 
 whereas for the triceps , the highest muscle strength and muscle activation were found at the 
 joint angle of 84. the results confirmed that muscle strength and muscle activation were 
 highest at the joint angle where concentric contraction was 20% more stretched than in the 
 resting point . nam21 measured muscle strength with elbow joint 
 flexion angles of 110 to 70 in 5-degree intervals , and the results showed that the smaller 
 the elbow joint flexion angle , the higher the rate of increase of muscle strength . so at a 
 joint angle of 70 , the rate of increase of muscle strength was the highest . the results for 
 muscle activation at biceps joint angles of 70 and 80 also agreed with those in the 
 present research , which showed that thee muscle activation at 70 was higher than that at 
 84. however , in nams21 research , the 
 angle at which muscle length was 20% stretched in relation to the resting point of the joint 
 was not considered . so nams21 research 
 data can not be generalized to all joints , whereas the advantage of the present research is 
 that it is applicable to all the other joints . as a result , the present research demonstrated that the total force at a joint angle 
 stretched 20% is greater than the total of the active force and passive force exerted in the 
 resting position . hence , regarding muscle - strength improving exercises , applying the maximum 
 resistance at a joint angle representing 20% muscle stretch in a more significant factor for 
 improving muscle strength than applying it at a joint angle representing a resting position . 
 nevertheless , this research was only performed with respect to the change in length - tension 
 curve of the elbow joint , so it is not easy to broaden the interpretation to all joints . therefore , in the future , we are considering performing research using the same method on 
 other joints by examining the muscle strength and muscle activation with a joint angle 
 representing 20% stretch from the resting position .
[ purpose ] this research investigated the relationship between elbow joint angle and 
 elbow flexor and extensor strength and activation , taking into consideration the 
 length - tension tension curve of the muscle . 
 [ subjects ] there were 30 research subjects in 
 total , 15 male and 15 female college students from busan s university who had no 
 functional disabilities that might affect measurement of muscle strength and muscle 
 activation , and none had they experienced any damage in their upper extremities or hands . 
 [ methods ] the elbow joint angles were positioned at angles of 56 , 70 and 84 , and then 
 muscle strength and activation were compared 
 . repeated measures anova was used for 
 statistical analysis , and the paired t - test was used to identify the difference between 
 each angle . 
 we used the spss for windows ( ver . 
 21.0 ) statistical software and a 
 significance level of =0.05 . 
 [ results ] the results showed that muscle strength and 
 activation of the biceps was highest when the joint was placed at 56. on the other hand , 
 for the triceps , the result was highest when the joint angle was placed at 84. 
 [ conclusion ] the tests confirmed that muscle strength and activation were highest at the 
 joint angle at which the muscle was stretched to 20% more than the resting position in 
 concentric contraction .