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Optical measurement of the center of rotation for human joints
OPTICAL MEASUREMENT OF THE CENTER ROTATION FOR HUMAN JOINTS*
OF
T. E. SHOUPt Department of Mechanical Engineering. University of Houston. Houston. TX 77004. U.S.A. Abstract-A photo-optical technique. based on the theory of Moire fringes. is presented for use in locating the two-dimensional instantaneous center of rotation for human joints. The technique is demonstrated for the motion of the human shoulder complex when undergoing elevation,
The instantaneous center of rotation for two objects undergoing relative motion in a plane is the location of a point on one body about which the other is instantaneously rotating (Shigley, 1969). It is sometimes convenient to be able to measure accurately the instantaneous center of rotation of human joints as they flex in two-dimensions (Taylor, 1968). Such kinematic information is especially important when reconstructive surgery is being considered or when prosthetic limb replacements are being designed. Often, the location of the instantaneous center of rotation of a joint will change position as the joint flexes. This “polycentric” action is often essential for changing the mechanical advantage of a limb-joint combination or for providing stability in the form of locking positions as in the case of the knee. The path of the instantaneous center of rotation as it moves is called a centrode. Traditional approaches to the study of joint motion have been based on X-ray studies or on photographs of pins implanted in the bone. Multiple X-ray exposures can present a radiation health hazard and have associated inaccuracies in the information they provide (Wolf, 1974). In addition, since prosthetic appliances are usually attached to external tissue (the motion of which may be somewhat different than the bone motion) it becomes important to be able to externally analyze joint motion. Photographic techniques alone can be difficult to use in determining the joint rotation center for closely spaced positions due to the inaccuracies associated with the poor intersection angles in the graphical constructions. The purpose of this Note is to demonstrate a reliable, accurate technique for determining joint instant centers of rotation. The technique is based on the theory of Moire fringe optics. Since this technique is a photo-optical method it does not interfere with the motion as would a technique utilizing an external linkage 1Kinzel er ol.. 1972). The d~~uble exposure image of a set of equally spaced lines in two adjacent, closely spaced positions. will generate a set of interference bands known as Moire fringes. The particular band where a line in * Rrceiced 10 Januor~~ 1975. t Associate Professor.
one position interferes with its image in another position is known as the P = 0 or “primary fringe.” It has been shown by Shoup and Steffen (1974) that this primary fringe passes through the pole of motion for the two positions. As the adjacent positions come close together. the pole of motion approaches the instantaneous center of rotation. In order to uniquely locate the center of rotation. two similar grid patterns are used to construct the target shown in Fig. 1. In each of these two grid patterns, one white band has been darkened in order to aid the identification of the primary fringe. This target, which is mounted on a piece of fiberboard for flatness, can be attached to a moving limb by means of elastic bands and bandage tape. A series of high contrast negatives is made for a sequence of equally spaced, adjacent limb positions. These negatives are then photographically printed in overlaying pairs as a double exposure to provide the two-dimensional, joint pivot center as demonstrated in Fig. 1. As the angle of rotation between positions becomes small, the fringes become spaced wider apart and thus are easier to identify. Because of this fact, a high degree of accuracy is possible even for closely spaced positions. To demonstrate the use of this technique, the motion of the human shoulder complex during elevation will be considered. Elevation occurs when the arm is raised outward from the side of the body. The twodimensional motion of the arm relative to the body is polycentric since the shoulder joint is composed
Fig. 1. The Moire fringe technique for measurement center of rotation for human joints. 241
of the
242
T. E.
SHOL’P
scapula
1
,- clavide cm.
@
acromiMavicular
@
ghobumeral
joint joint
@J stertwciavikufar
joint
Fig. 2. The anatomy of the shoulder complex.
of four independent articulations. The structure of the shoulder complex is shown in Fig. 2 (Gray, 1974). The acromioclavicular joint exists at the point where the clavicle meets the acromion process of the scapula. The glenohumeral joint is the ball and socket joint where the humerus mates with the glenoid cavity of the scapula. The sternoclavicular joint exists where the clavicle meets the sternum. The scapulothoracic joint, which does not appear in Fig. 2, exists on the back side of the body where the scapula rotates on the thorax. Previous studies of the shoulder (Inman et al., 1944) have demonstrated how each of these four articulations contribute in concert to the total motion of the extremity. To establish a fixed frame of reference for the body, the protruding spinous process of the 7th cervical vertebrae was used as the origin for a coordinate system having its vertical axis aligned with the vertical axis of the body. The prominent spinous process of the 7th cervical vertebrae lies close to the surface of the skin near the base of the neck and is easily identified. Since the skin over this point does not displace substantially during arm elevation, its location was marked with a dark adhesive dot for purposes of the photographic tests. Elevation data results obtained from an adult male of height 170cm are presented in Fig. 3. The extension range for this data is 3&180 deg. The initial data point, located near to the vertical axis, corresponds to 30 deg of extension. As the angle of extension increases, the centrode curves upward to the right. This behavior indicates that the initial phase of extension is strongly dependent on the scapulothoracic and sternoclavicular joints and that later, the motion becomes more dependent on the glenohumeral and acromioclavicular articulations. This is in agreement with the findings of Inman, Saunders, and Abbott (1944) who reported a two to one ratio between the rotation of these two joint pairs for elevation beyond 30 deg.
-10
0
IQ
20
30
40
cm.
Fig. 3. The centrode path for the human shoulder complex during elevation of the right arm.
It should be noted that the centrode shape during elevation is strongly a function of individual style. This is because the shoulder mechanism is a multiple degree of freedom system. The individuality of this motion strongly suggests the need for careful study when this motion is of medical concern. This also indicates the desirability of having a simple, reliable method, such as the one herein presented, to measure the centrode of motion. With suitable attachment fixtures, the MoirC fringe technique can be used to measure the centrodes associated with other joints such as the knee, elbow, wrist, jaw, etc. Acknowledgemen-The author gratefully acknowledges the financial support of the National Science Foundation through grant GK-35521.
REFERENCES
Gray, H. (1974) Anatom!. Descriptise and Surgical. Running Press. Philadelphia. PA. Inman. V. T.. Saunders, J. B. and Abbott, L. C. (1944) Observations on the Function of the Shoulder Joint. J. Bone Jnr. Surq. 26. 1. l-30. Kinzel. G. L.. Hillberry. B. M.. Hall, A. S., Van Sickle, D. C. and Harvey, W. M. (1972) M,easurement off the total motion between two body segments-II. Description of application. J. Bionlechanics 5, 283-293. Shigley. J. E. (1969) Kinemafic Anol.vsis of Mechanisms, 2nd Edn.. p. 83. McGraw-Hill. NY. Shoun. T. E. and Steffen. J. R. (1974) On the use of Moirt frin’ge patterns for the expeiimenial kmematic analysis of olane motion. Mechunism und Machine Theory 9, 131’140. Taylor, C. L. (1968) The biomechanics of the normal and of the amputated upper extremity. Human Limbs and their Substitutes (Edited by Klopsteg. P. and Wilson, P. D.), pp. 169-221. Hafner. NY. Wolf, B. (1974) Distortion incurred in a sequence of radiographs of an articulating joint. J. Biomechanics 7. 155-156.
OF
T. E. SHOUPt Department of Mechanical Engineering. University of Houston. Houston. TX 77004. U.S.A. Abstract-A photo-optical technique. based on the theory of Moire fringes. is presented for use in locating the two-dimensional instantaneous center of rotation for human joints. The technique is demonstrated for the motion of the human shoulder complex when undergoing elevation,
The instantaneous center of rotation for two objects undergoing relative motion in a plane is the location of a point on one body about which the other is instantaneously rotating (Shigley, 1969). It is sometimes convenient to be able to measure accurately the instantaneous center of rotation of human joints as they flex in two-dimensions (Taylor, 1968). Such kinematic information is especially important when reconstructive surgery is being considered or when prosthetic limb replacements are being designed. Often, the location of the instantaneous center of rotation of a joint will change position as the joint flexes. This “polycentric” action is often essential for changing the mechanical advantage of a limb-joint combination or for providing stability in the form of locking positions as in the case of the knee. The path of the instantaneous center of rotation as it moves is called a centrode. Traditional approaches to the study of joint motion have been based on X-ray studies or on photographs of pins implanted in the bone. Multiple X-ray exposures can present a radiation health hazard and have associated inaccuracies in the information they provide (Wolf, 1974). In addition, since prosthetic appliances are usually attached to external tissue (the motion of which may be somewhat different than the bone motion) it becomes important to be able to externally analyze joint motion. Photographic techniques alone can be difficult to use in determining the joint rotation center for closely spaced positions due to the inaccuracies associated with the poor intersection angles in the graphical constructions. The purpose of this Note is to demonstrate a reliable, accurate technique for determining joint instant centers of rotation. The technique is based on the theory of Moire fringe optics. Since this technique is a photo-optical method it does not interfere with the motion as would a technique utilizing an external linkage 1Kinzel er ol.. 1972). The d~~uble exposure image of a set of equally spaced lines in two adjacent, closely spaced positions. will generate a set of interference bands known as Moire fringes. The particular band where a line in * Rrceiced 10 Januor~~ 1975. t Associate Professor.
one position interferes with its image in another position is known as the P = 0 or “primary fringe.” It has been shown by Shoup and Steffen (1974) that this primary fringe passes through the pole of motion for the two positions. As the adjacent positions come close together. the pole of motion approaches the instantaneous center of rotation. In order to uniquely locate the center of rotation. two similar grid patterns are used to construct the target shown in Fig. 1. In each of these two grid patterns, one white band has been darkened in order to aid the identification of the primary fringe. This target, which is mounted on a piece of fiberboard for flatness, can be attached to a moving limb by means of elastic bands and bandage tape. A series of high contrast negatives is made for a sequence of equally spaced, adjacent limb positions. These negatives are then photographically printed in overlaying pairs as a double exposure to provide the two-dimensional, joint pivot center as demonstrated in Fig. 1. As the angle of rotation between positions becomes small, the fringes become spaced wider apart and thus are easier to identify. Because of this fact, a high degree of accuracy is possible even for closely spaced positions. To demonstrate the use of this technique, the motion of the human shoulder complex during elevation will be considered. Elevation occurs when the arm is raised outward from the side of the body. The twodimensional motion of the arm relative to the body is polycentric since the shoulder joint is composed
Fig. 1. The Moire fringe technique for measurement center of rotation for human joints. 241
of the
242
T. E.
SHOL’P
scapula
1
,- clavide cm.
@
acromiMavicular
@
ghobumeral
joint joint
@J stertwciavikufar
joint
Fig. 2. The anatomy of the shoulder complex.
of four independent articulations. The structure of the shoulder complex is shown in Fig. 2 (Gray, 1974). The acromioclavicular joint exists at the point where the clavicle meets the acromion process of the scapula. The glenohumeral joint is the ball and socket joint where the humerus mates with the glenoid cavity of the scapula. The sternoclavicular joint exists where the clavicle meets the sternum. The scapulothoracic joint, which does not appear in Fig. 2, exists on the back side of the body where the scapula rotates on the thorax. Previous studies of the shoulder (Inman et al., 1944) have demonstrated how each of these four articulations contribute in concert to the total motion of the extremity. To establish a fixed frame of reference for the body, the protruding spinous process of the 7th cervical vertebrae was used as the origin for a coordinate system having its vertical axis aligned with the vertical axis of the body. The prominent spinous process of the 7th cervical vertebrae lies close to the surface of the skin near the base of the neck and is easily identified. Since the skin over this point does not displace substantially during arm elevation, its location was marked with a dark adhesive dot for purposes of the photographic tests. Elevation data results obtained from an adult male of height 170cm are presented in Fig. 3. The extension range for this data is 3&180 deg. The initial data point, located near to the vertical axis, corresponds to 30 deg of extension. As the angle of extension increases, the centrode curves upward to the right. This behavior indicates that the initial phase of extension is strongly dependent on the scapulothoracic and sternoclavicular joints and that later, the motion becomes more dependent on the glenohumeral and acromioclavicular articulations. This is in agreement with the findings of Inman, Saunders, and Abbott (1944) who reported a two to one ratio between the rotation of these two joint pairs for elevation beyond 30 deg.
-10
0
IQ
20
30
40
cm.
Fig. 3. The centrode path for the human shoulder complex during elevation of the right arm.
It should be noted that the centrode shape during elevation is strongly a function of individual style. This is because the shoulder mechanism is a multiple degree of freedom system. The individuality of this motion strongly suggests the need for careful study when this motion is of medical concern. This also indicates the desirability of having a simple, reliable method, such as the one herein presented, to measure the centrode of motion. With suitable attachment fixtures, the MoirC fringe technique can be used to measure the centrodes associated with other joints such as the knee, elbow, wrist, jaw, etc. Acknowledgemen-The author gratefully acknowledges the financial support of the National Science Foundation through grant GK-35521.
REFERENCES
Gray, H. (1974) Anatom!. Descriptise and Surgical. Running Press. Philadelphia. PA. Inman. V. T.. Saunders, J. B. and Abbott, L. C. (1944) Observations on the Function of the Shoulder Joint. J. Bone Jnr. Surq. 26. 1. l-30. Kinzel. G. L.. Hillberry. B. M.. Hall, A. S., Van Sickle, D. C. and Harvey, W. M. (1972) M,easurement off the total motion between two body segments-II. Description of application. J. Bionlechanics 5, 283-293. Shigley. J. E. (1969) Kinemafic Anol.vsis of Mechanisms, 2nd Edn.. p. 83. McGraw-Hill. NY. Shoun. T. E. and Steffen. J. R. (1974) On the use of Moirt frin’ge patterns for the expeiimenial kmematic analysis of olane motion. Mechunism und Machine Theory 9, 131’140. Taylor, C. L. (1968) The biomechanics of the normal and of the amputated upper extremity. Human Limbs and their Substitutes (Edited by Klopsteg. P. and Wilson, P. D.), pp. 169-221. Hafner. NY. Wolf, B. (1974) Distortion incurred in a sequence of radiographs of an articulating joint. J. Biomechanics 7. 155-156.