functional reach ( fr ) is a very important motion because it is often performed in daily 
 life . fr distance is reportedly 
 correlated with the center of pressure ( cop ) excursion2 ; cop was used as the operational definition of center of gravity 
 ( cog ) . however , jonsson et al . found no significant correlation between the reach distance and 
 cop6 . therefore , fujisawa et al . 
 developed an fr model and clarified the optimal posture that could move the fingertip 
 farthest forward while standing7 . the 
 simulation showed that when the height was 170  cm , a postural change could elicit a reach of 
 approximately 25  cm during fr , without moving cog forward . in addition , the maximal fr 
 ( frmax ) increased in proportion to height . increase in foot length proportional to height 
 and cog movement was important for this increase . in addition , with a fixed cog , the 
 relationship between the joint angles of each frmax did not depend on height . during rehabilitation , patients are often trained in the kneeling position8 , as this possibly strengthens the ability of 
 hip joint control . although patients can move cop to the front of the ankle joint while 
 standing , they are unable to move cop to the front of the knee joint while kneeling . therefore , reaching forward while maintaining balance in the kneeling position is 
 difficult . during fr , this is because the 
 number of degrees of freedom of the reaching task is at least 3 in comparison to the 
 2-dimensional sagittal plane . if the optimal posture for maximum reaching forward can be 
 estimated , it can be applied to the practice of physical therapy , i.e. , using fr models , 
 postural control and optimal postural control exercises can be evaluated by referring to the 
 estimated values . the purpose of the present study was to examine the validity of the fr models by comparing 
 actual values with estimated values . twenty - eight volunteers participated in this study ( males : 14 , females : 14 , age : 21  
 1  years , height : 166.8  9.0  cm , and body mass : 60.1  8.5  kg ) , all of whom provided written 
 informed consent prior to participation ; the human subjects ethics committee of tohoku bunka 
 gakuen university approved the study ( no . an algorithm was developed to identify optimal posture during fr with a 4-segment geometric 
 model . in this model , optimal posture is adopted to maximize fr , and the movement taken to 
 adopt such a posture is referred to as postural optimization . the segments of the fr model 
 for standing ( fr model - s , fig . 1fig . 1.functional reach model for standing ( fr model - s)cog : center of gravity , hat : head , arm , and trunk , l / e : lower extremity , 
 1 : length of thigh and leg , 2 : length of trunk , 
 3 : length of upper extremity , r1 : length from ankle to cog of 
 lower extremity , r2 : length from hip to cog of hat ,  ,  ,  : clockwise 
 direction is a plus ) consisted of the unilateral upper extremity ( reaching arm ) , the head , unilateral 
 arm , and trunk ( hat ) , and the 2 lower extremities ( i.e. , thigh , leg , and foot ) . the angles 
 of the generalized coordinate system  ,  , and  , as well as other parameters , were used as 
 variables ( fig . in addition , the origin of the 
 coordinate was set at the ankle joint . both  and  were calculated by knowing  and gx ( the 
 cog position ) ( appendix 1 ) . as a result , the optimal posture for the farthest reach possible 
 and the maximum forward fingertip position ( ftxmax ) was decided . the fr model for kneeling 
 ( fr model - k , fig . 2.functional reach model for kneeling ( fr model - k)cog : center of gravity , hat : head , arm and trunk , 1 : length of leg , 
 2 : length of thigh , 3 : length of trunk , 4 : 
 length of upper extremity , r1 : length from knee joint to cog of leg and 
 foot , r2 : length from knee joint to cog of thigh , r3 : length 
 from hip joint to cog of hat ,  ,  ,  : clockwise direction is a plus ) consisted of the unilateral upper extremity ( reaching arm ) , the head , unilateral 
 arm , and trunk ( hat ) , and the 2 lower extremities ( i.e. , thigh , leg , and foot ) . the origin 
 of the coordinate was set at the knee joint in the fr model - k ( fig . both  and  were calculated by knowing  and gx , as in the 
 fr model - s ( appendix 2 ) . as a result , we were able to determine the optimal posture for the 
 furthest reach possible and ftxmax . functional reach model for standing ( fr model - s ) cog : center of gravity , hat : head , arm , and trunk , l / e : lower extremity , 
 1 : length of thigh and leg , 2 : length of trunk , 
 3 : length of upper extremity , r1 : length from ankle to cog of 
 lower extremity , r2 : length from hip to cog of hat ,  ,  ,  : clockwise 
 direction is a plus functional reach model for kneeling ( fr model - k ) cog : center of gravity , hat : head , arm and trunk , 1 : length of leg , 
 2 : length of thigh , 3 : length of trunk , 4 : 
 length of upper extremity , r1 : length from knee joint to cog of leg and 
 foot , r2 : length from knee joint to cog of thigh , r3 : length 
 from hip joint to cog of hat ,  ,  ,  : clockwise direction is a plus ftxmax was simulated with an original program by using matlab ( 2014b , mathworks , japan ) . the height was set to 150 , 160 , 170 , 180 , and 190  cm . in the fr model - s , gx changed from 0% 
 to 60% of the foot length and  from 0 to 70. in the fr model - k , gx changed from 0  cm to 
 10  cm and  from 0 to 70. for fr model - s , a martin - type anthropometer and goniometer was 
 used to measure 1 ( trochanter - malleolus distance ) , 2 ( distance between the acromion and 
 the greater trochanter ) , 3 ( upper limb length ) , sg length ( distance between the clavicular 
 head and the acromion ) , and sg range of motion ( rom ) ( flexion of the shoulder girdle ) . for 
 fr model - k , a martin - type anthropometer and goniometer was also used to measure 1 ( lower 
 leg length ) , 2 ( thigh length ) , 3 ( distance between the acromion and the greater 
 trochanter ) , 4 ( upper limb length ) , sg length ( distance between the clavicular head and the 
 acromion ) , and sg rom ( flexion of the shoulder girdle ) . , a 
 tape marker was affixed to the acromion , greater trochanter , lateral epicondyle of the 
 femur , and lateral malleolus . the subjects stood on a tag tile sensor ( huge - mat , nitta , 
 japan ) for cop measurement , which was used as an operational definition of cog . the lateral malleolus while standing or the lateral epicondyle of the 
 femur while kneeling was also matched to zero position of the original equipment ( fig . 3fig . 3.functional reach and equipment for measurementa : functional reach while standing , b : functional reach while kneeling ) . the subjects reached forward with the dominant upper extremity , which was defined 
 as the side used for holding chopsticks . based on a simulation , the subjects were instructed 
 in the standing position reach as follows : 1 ) do reach as far forward as possible , 2 ) do 
 raise your arm higher than your ear , and 3 ) do not pull your buttocks backward . the subjects 
 were also instructed in the kneeling position reach as follows : 1 ) do reach as far forward 
 as possible , 2 ) do raise your arm higher than your ear , and 3 ) do pull your buttocks 
 backward slightly . the fr motion was also recorded using a digital video camera ( ivis- hv30 , 
 canon , japan ) . the cog position ( gx ) was 
 measured when the subjects attained maximum forward reach . moreover , the joint angles were 
 determined using a video analysis system ( dartfish 4.5.2.0 , dartfish , japan ) . in addition , actual hip joint angle was used 
 as a restriction condition of . the measurement value was substituted for the segment 
 length : 1 , 2 , 3 , and 4 . the validity of the fr model was considered based on the 
 relationship between actual ftxmax data and estimated ftxmax data , and between actual joint 
 angles and estimated joint angles . functional reach and equipment for measurement a : functional reach while standing , b : functional reach while kneeling pearson s product moment correlation coefficient ( r ) was calculated between the actual 
 ftxmax and estimated data . the actual ftxmax was 112.1  7.1  cm during fr while standing , and the estimated ftxmax was 
 109.3  7.0  cm . the actual shoulder joint angle was 141.5  5.7 and the estimated angle was 
 136.4  4.8. the actual ankle joint angle was 0.2  1.7 and the estimated angle was 3.0  
 1.6. the correlation coefficients between the actual data and the estimated data for 
 ftxmax , shoulder joint angle , and ankle joint angle were 0.93 ( p<0.01 ) , 0.83 ( p<0.01 ) , 
 and 0.73 ( p<0.01 ) , respectively ( table 
 1 
 table 1.ftxmax , joint angles , and gx during functional reach ) . the actual ftxmax was 90.9  5.9  cm during fr while kneeling , and the estimated ftxmax was 
 90.5  6.1  cm . the actual shoulder joint angle was 134.5  8.9 and the estimated angle was 
 128.6  6.1. the actual knee joint angle was 110.7  4.5 and the estimated angle was 115.0 
  3.9. the correlation coefficients between the actual data and the estimated data for 
 ftxmax , shoulder joint angle , and knee joint angle were 0.86 ( p<0.01 ) , 0.81 ( p<0.01 ) , 
 and 0.72 ( p<0.01 ) , respectively ( table1 ) . in results for simulation of fr while standing , ftxmax increased in proportion to height 
 and gx position ( fig . 4.relationship between gx and ftxmax and joint angles in the 
 optimal posture . a : fr model - s , b : fr model - k , gx : x - coordinate of center of gravity , 
 ftxmax : maximum forward fingertip position ) . when gx was 60% of the foot length , ftxmax was 103.3  cm at a height of 150  cm and 
 130.3  cm at a height of 190  cm . furthermore , when gx was 60% of the foot length , the optimal 
 posture at 190  cm was 165.1 of shoulder flexion , 60.0 of hip flexion , and 2.5 of ankle 
 plantar flexion . in contrast , when gx was 0% of the foot length ( gx=0  cm ) , ftxmax was 
 87.3  cm at a height of 150  cm and 110.6  cm at a height of 190  cm . furthermore , when gx was 
 60% of the foot length , the optimal posture at 190  cm was 163.0 of shoulder flexion , 68.7 
 of hip flexion , and 13.8 of ankle plantar flexion . . a : fr model - s , b : fr model - k , gx : x - coordinate of center of gravity , 
 ftxmax : maximum forward fingertip position in the results for simulation of fr while kneeling , ftxmax increased in proportion to 
 height and decreased in proportion to the backward movement of the gx position ( fig . when gx was 0  cm , ftxmax was 89.0  cm at a 
 height of 150  cm and 112.7  cm at a height of 190  cm . moreover , when gx was 0  cm , the optimal 
 posture at 190  cm was 158.9 of shoulder flexion , 75.4 of hip flexion , and 113.6 of knee 
 flexion . in contrast , when gx was 10  cm , ftxmax was 75.2  cm at a height of 150  cm and 
 99.1  cm at a height of 190  cm . moreover , when gx was 10  cm , the optimal posture at 190  cm 
 was 153.6 of shoulder flexion , 82.7 of hip flexion , and 127.1 of knee flexion . in this study , the validity of the fr model was clear because the correlation coefficients 
 between actual ftxmax and estimated ftxmax , a well as between the joint angles , were very 
 high . because ankle joint function decreases in the elderly and in people with disability , 
 these individuals often can not move gx far enough forward . physical therapists have to draw 
 out a patient s ability to the maximum , and must be able to instruct on the optimal postural 
 control strategy in a given cog position . we therefore postulated that the fr model can use 
 not only individual optimization but also general strategic examination . as an exercise of postural control , fr while kneeling is unique . during fr in the kneeling 
 position , individuals are unable to move gx forward ; however , gx can be moved forward in the 
 standing position . ftxmax decreases in proportion to amount of backward movement of gx in 
 the kneeling position . although ftxmax is the highest when gx is 0  cm in the kneeling 
 position , it is the lowest when gx is 0  cm in the standing position . moreover , we found that 
 when gx was 0  cm , the optimal posture at 190  cm was 113.6 of knee flexion in the kneeling 
 position and 2.5 of ankle plantar flexion in the standing position . in other words , although individuals who do 
 not pull their buttocks backward are able to reach farther while standing , individuals who 
 pull their buttocks backward can reach farther while kneeling . because ftxmax is the highest when gx is 0  cm in the kneeling position , the gravitational 
 torque at the knee joint is very low during this posture . in contrast , because ftxmax is the highest when gx is forward in 
 the standing position , the gravitational torque at the ankle joint is very high during this 
 posture . as a result furthermore , angle  is generally larger in the standing position than in the kneeling 
 position ; thus , the gravitational torque at the hip joint is larger in the standing position 
 than in the kneeling position during maximum forward reach . therefore , the standing position 
 requires greater muscle activity than the kneeling position . from the viewpoint of balance , the anteroposterior length of the base of support is longer 
 in the kneeling position than in the standing position . however , the maintenance of balance 
 in the kneeling position is very difficult during maximum forward reach because the center 
 of movement of the knee joint is close to the end of the base of support . postural 
 adjustment is very difficult during maximum forward reach while kneeling because the muscle 
 torque of the knee joint is almost zero , as described above . in conclusion , the validity of both fr models for estimating optimal posture was confirmed . therefore , the fr model is useful for the evaluation of postural control and optimal 
 postural control exercises .
[ purpose ] the purpose of the present study was to examine the validity of functional 
 reach models by comparing actual values with estimated values . [ subjects and methods ] 
 twenty - eight volunteers 
 were included in this study ( male : 14 , female : 14 , age : 21  
 1  years , height : 166.8  9.0  cm , and body mass : 60.1  8.5  kg ) . the maximum forward 
 fingertip position and joint angles were measured using the original equipment . in 
 addition 
 , the maximum forward fingertip position , shoulder joint angle , and knee or ankle 
 joint angle were estimated using the functional reach model . 
 [ results ] the correlation 
 coefficients between actual data and estimated data for the maximum forward fingertip 
 position , shoulder joint angle , and ankle joint angle while standing were 0.93 , 0.83 , and 
 0.73 , respectively . 
 the correlation coefficients between actual data and estimated data 
 for the maximum forward fingertip position , shoulder joint angle , and knee joint angle 
 while kneeling were 0.86 , 0.81 , and 0.72 , respectively . 
 [ conclusion ] the validity of both 
 functional reach models in estimating optimal posture was confirmed . 
 therefore , the 
 functional reach model is useful for evaluation of postural control and optimal postural 
 control exercises .