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The Influence of Four-Bar Linkage Knees on Prosthetic Swing-Phase Floor Clearance

Steven A. Gard, PHD
Dudley S. Childress, PHD
Jack E. Uellendahl, CPO

ABSTRACT

Four-bar linkage knees provide greater toe clearance daring the swing phase of walking than do single-axis knees. The authors developed a computer model of a transfemoral prosthesis that allowed the kinematics of commercially available four-bar linkage knees and a single-axis knee to be simulated so leg-shortening could be characterized.

A plot of hip-toe distance versus knee-flexion angle demonstrated four-bar knees are able to shorten the limb with less knee flexion than is needed using a single-axis knee. For a hip-knee angle combination at the time of minimum toe clearance daring normal walking, contour plots revealed the four-bar knees have 0.9-3.2 cm greater toe clearance than do single-axis knees.

Introduction

More than 100 individual knee mechanisms are commercially available for the North American amputee population (I). Classifications for prosthetic knees have been proposed previously (1,2), but there are two basic knee categories of kinematic function into which prosthetic knees fall: single-axis knees and polycentric knees. Prosthetists should be aware of several key differences between these two classes of knees to make informed decisions regarding prescriptions of prosthetic knees for their patients.

Single-axis knees have a single axis of rotation about which the shank rotates with respect to the thigh. Polycentric knees, on the other hand, are characterized by a center of rotation that varies with the knee-flexion angle (1,2). The center of rotation, more appropriately called the instantaneous center of rotation, is simply the point about which the shank and foot rotate as the knee flexes. Polycentric knees are becoming increasingly popular among prosthetists for transfemoral amputee prostheses.

The most common type of polycentric knee is the four-bar linkage knee, so-called because it has four axes of rotation connected by four rigid linkages. The polycentric nature of four-bar linkage knees accounts for two key advantages: stance-phase stability (3-5) and knee-flexion cosmesis (1,2,6). A lesser known distinction of four-bar linkage knees is their inherent ability to provide greater foot clearance than single-axis knees for a given knee-flexion angle (6). This additional floor clearance allows the amputee to walk with less concern for floor clearance during prosthetic swing. This article focuses primarily on floor clearance issues of four-bar and single-axis knees but also includes brief discussions of stance-phase stability and cosmesis.

Stance-Phase Stability and Cosmesis

The stability of a four-bar knee during load-bearing is determined by the location of the instantaneous center of rotation with respect to the ground reaction force vector. Prosthetists are afforded some control over the degree of stability through prosthetic alignment (5).

Figure 1 shows a lateral view of a typical four-bar linkage knee with locations of the instant centers of rotation plotted at 5-degree increments of knee flexion. Points A, B, C and D represent the axes of rotation of the four-bar knee. The instantaneous center of rotation is determined by intersecting the line through points A and B with the line through points C and D.

A four-bar knee may be considered dynamically equivalent to a single-axis knee having its axis of rotation at the instantaneous center of rotation. During the stance phase, the instantaneous center of rotation of the four-bar knee must be posterior to the load line- which is not to be confused with the alignment line-so the knee will maintain an extension moment. This ordering is illustrated in Figure 2 , which shows a video frame image of a bilateral transfemoral amputee during right single stance with lines drawn to show the four-bar knee's instant center of rotation (at the crossing point) and the orientation of the ground reaction force vector (anterior to the instant center). For more information on four-bar linkage knee stability, the reader is referred to Radcliffe (3-5).

Some four-bar knees have been designed specifically to address the cosmetic needs of knee disarticulation amputees and amputees with extremely long transfemoral residual limbs (1,6). These four-bar knees minimize the protrusion at the distal end of the socket when the patient is sitting. They are characterized by long anterior and posterior linkages (see Figure 3 ) designed to allow the shin to fold behind the thigh at 90 degrees.

Floor Clearance

This article presents the results of a research study demonstrating four-bar linkage knees provide greater floor clearance than do single-axis knees. A computer model of a transfemoral prosthesis was developed into which representations of commercially available four-bar linkage knees were "inserted" for evaluation. The computer simulated the swing-phase kinematics of the prosthesis by rotating the hip and knee through the full ranges of motion while calculating leg parameters such as the hip-toe distance and floor clearance.

The shortening characteristics of the four-bar linkage knees were compared with those of a single-axis knee to show the differences in floor clearance. The information presented is not intended to be used for the selection of a particular four-bar linkage knee, which must be decided on the basis of many factors, but to show the distinct advantage these knees have over single-axis knees for increasing floor clearance.

Method of Analysis

The investigation was limited to a sagittal-plane kinematic analysis of a select number of commercially available four-bar linkage knees subject to the following criteria:

• commercially available during 1994 with plans to continue marketing the knee in 1995;
• endoskeletal units;
• adult knees;
• linkages having constant length throughout the knee-flexion range; and
• four-bar linkage knee function during the swing phase.

The following knees were included in the study: Hosmer UltraRoeLite, Hosmer VC, Ohio Willow Wood Pendulum Senior, Otto Bock 3R23 Knee Disarticulation, Otto Bock 3R36 Habermann, Otto Bock 3R60, Otto Bock SR7O and USMC OHC d The Otto Bock 3R36 and R70 both have adjustable knee-extension stops; therefore, each knee was analyzed in its stable and least stable alignment positions.

A computer program was developed (7) using the model of the transfemoral prosthesis shown in Figure 4 to analyze the swing-phase kinematics of the four-bar linkage knees. The foot was assumed to be a 27.0-cm SACH aligned with an 18.0-mm heel. The dimensions of the model were based on anthropomorphic data for a 50th-percentile man (8), which placed the elevation of the hip center at 92.85 cm above the floor and the elevation of the cosmetic knee center at 49.45 cm.

The alignment used for the computer model is one recommended by Otto Bock in which the alignment reference line passes through the hip center, the knee-alignment point (point C in Figure 4 ) and a point 15.0 mm posterior to the foot's anterior-posterior midpoint. The knee alignment point is simply that point lying on the line between the hip center and the foot's alignment point at the elevation of the anatomic knee center. This method of alignment was selected because of the success the last-named author has had with it in fitting transfemoral amputee patients and because it is the method taught in the Prosthetic-Orthotic Center of the Northwestern University Medical School (9).

The computer program required information regarding dimensions, alignment and orientation for each four-bar knee, resulting in the numerical representation of a particular knee's design. The complete transfemoral prosthesis computer model was constructed by overlaying the manufacturer's recommended alignment point (in the knee's computer representation) onto the model's knee alignment point (see Figure 4 ). For the four-bar knees included in the study, the manufacturer's recommended alignment point was either at point C or at the midpoint of the line connecting points A and C (see Figure 1 ).

The computer program simulated the first 70 degrees of knee flexion, and hip flexion from -20 to 30 degrees at 1-degree increments. Leg kinematic parameters, including positions of points on the leg and floor clearance, were calculated for all combinations of the hip and knee angles. The elevation of the hip was held constant at the level of standing throughout the analysis, an assumption important for the calculation of floor clearance.

Knee-flexion angle often is defined as the angle between the longitudinal axes of the thigh and shank. However according to this definition, any fourbar linkage knee designed as a parallelogram (i.e., opposite sides have equal length) will always have a knee-flexion angle of 0 degrees, even though the linkage mechanism rotates, because the shank axis will move parallel to the thigh axis.

While no commercially available fourbar linkage knees have a parallelogram design, a few designs approximate one, For these parallelogram-like knees, use of the conventional definition of the knee-flexion angle would cause a bias because it would appear as though greater floor clearance could be achieved with less knee flexion. Consequently, another definition of knee-flex. ion angle is used to remove this bias.

The knee-flexion angle was defined to be 0 when the knee was at full extension and assumed to increase linearly with the angle formed by the lines connecting the hip center with the knee alignment point and the knee alignment point with the solid-ankle center (see Figure 5 ). The maximum differences between the knee-flexion angles, as calculated for these two definitions, approached 10 degrees for those fourbar linkage designs that approximated parallelograms, but, for the majority of knees, the difference was less than 5 degrees over the range of knee motion investigated.

The distance between the hip and the toe (hip-toe distance) was calculated as a function of the knee angle during the computer simulation. This leg parameter is a direct indicator of toe clearance during the swing phase of walking. For swing-through of the leg to occur without the toe coming into contact with the floor, the hip-toe distance must be made shorter than the distance from the hip to the floor.

A relatively simple explanation was devised to account for most of the additional hip-toe distance shortening that is observed in the four-bar linkage knees. The effect of a particular fourbar knee on the foot's trajectory, which determines toe clearance, can be described in terms of two rotations and a translation (see Figure 5 ). The computer program that performed the simulation also calculated an apparent ankle dorsiflexion angle and an apparent shank-shortening translation as a function of the knee-flexion angle. The ankle dorsiflexion and shank shortening are referred to as "apparent" because they do not physically occur, but the trajectory of the foot with respect to the thigh is such that these events are functionally perceived.

This approach was found to be a useful and informative method for characterizing the behavior of four-bar knees because it allowed the trajectory of the foot with respect to the thigh to be described independently of shank movement. Characterizing four-bar linkage knees in this manner suggests they are functionally similar to kinematically coupled knee-ankle mechanisms (e.g., Hydracadence leg).

The single-axis knee simulation was performed using the same transfemoral prosthesis computer model employed for the four-bar linkage knees. The single-axis knee was aligned in the model by placing the center of rotation at the elevation of the anatomic knee center, 1.5 cm posterior to the Otto Bock alignment line. The knee-flexion angle for the single-axis knee was defined as o degrees at full extension and was assumed to increase linearly with the angle formed by the longitudinal axes of the thigh and shank.

Results

Figure 6 shows how hip-toe distance varied as a function of the knee-flexion angle for the four-bar knees and the single-axis knee. The "5" designation in the graph's legend for the Otto Bock 3R36 and 3R70 indicates the most stable alignment position of the two tested for these knees. In all cases the hip-toe distances for the four-bar knees were less than those of the single-axis knee at given knee-flexion angles.

Figure 6 reveals that for the transfemoral prosthesis having a single-axis knee, the hip-toe distance increased during the first 20 degrees of knee flexion, shortened to its standing length at about 40 degrees, but didn't shorten sufficiently for toe clearance until the knee flexed to about 50 degrees. However, the hip-toe distances for the four-bar knees shortened sufficiently for toe clearance with smaller knee-flexion angles than was required with the single-axis knee. The knee-flexion angle necessary for clearance is dependent on the particular four-bar knee's linkage design.

It is from this additional shortening of the hip-toe distance that four-bar knees are able to provide increased floor clearance over single-axis knees. The four-bar knees produce shorter hip-toe distances than does the single-axis knee for a given knee-flexion angle because of the former's apparent shank-shortening and apparent ankle dorsiflexion. Another factor that contributes to the increased shortening of the hip-toe distance by the four-bar knees is a more anteriorly situated center of rotation relative to that of the single-axis knee over much of the kneeflexion range.

The apparent movements that describe the trajectory of the prosthetic foot with respect to the thigh are shown in Figure 7 and Figure 8 . Figure 7 shows how the effective shank length varies with respect to the knee-flexion angle for the four-bar knees. The greatest amount of apparent shank-shortening was achieved by the Otto Bock 3R23.

The shank length apparently shortened for only a few of the knees; for the others it lengthened. However, the magnitude of this effective length change is only on the order of a few millimeters, which made it a secondary factor by which floor clearance was increased.

The apparent ankle dorsiflexion (see Figure 8 ) of the four-bar knees was determined to be the most significant factor by which foot clearance was increased over that of the single-axis knee. As indicated in the graph in Figure 8 , the greatest apparent ankle dorsiflexion was achieved by the USMC OHC. The magnitude of the effect of apparent ankle dorsiflexion on the hiptoe distance and toe clearance is on the. order of centimeters.

Floor clearances were calculated for all combinations of the hip and kneel angles for the four-bar knees and the single-axis knee. These results have been summarized in toe-clearance contour plots (see Figure 9 ). The contours spaced at 1-cm intervals of floor clearance, show the first 5 cm of toe clearance for the various hip-knee angle combinations. The area that is bound by the innermost contour represents the level of the floor over which toe clearance is 0. The contour bounding the region of the floor represents those points at which the toe just barely contacts the floor. Moving outward from the first contour, each contour crossed represents an additional 1-cm increase in toe clearance. Values between contour lines may be linearly approximated to an accuracy within several millimeters.

Figure 10 is the enlarged contour plot for the single-axis knee. Winter (10) has reported that at the time of minimum toe clearance during normal walking, the swing-leg hip- and knee-flexion angles are 23 degrees and 49 degrees, respectively. These joint angles are indicated on the graph by dashed lines. The amount of toe clearance for this particular hip/knee angle combination is determined by the location of the point on the graph where these lines intersect. The point of intersection lies between the first and second contours, which means toe clearance is somewhere between 0 and 1 cm. A more accurate estimate for the amount of toe clearance can be obtained by linearly interpolating between the two contour lines, which yields a toe clearance value of approximately 0.6-0.7 cm. The actual value of toe clearance for the single-axis knee model, obtained from the toe-clearance data file created by the computer program, is 0.6 cm.

Figure 11 shows values of toe clearance from the computer simulations for the combination of hip and knee angles at the time of critical toe clearance during swing. The prosthetic knees are listed from left to right in order of decreasing toe clearance. Winter reported a mean minimum toe clearance of 1.29 cm for the group of normal subjects he investigated, indicated in Figure 11 for comparison. The USMC OHC provided approximately 3.8 cm of toe clearance whereas the single-axis knee was able to provide only 0.6 cm. The fourbar knee that had the least amount of toe clearance still provided 0.9 cm more clearance than the single-axis knee. All of the four-bar knees provided more toe clearance than the reported amount for normal walking.

Implications of Results

Several factors are involved in selecting the most appropriate knee for a particular patient. When deciding between single-axis knee and a four-bar linkage knee, one of the factors considered should be the amount of floor clearance during swing Amputees using four-bar knees, which provide increased toe clearance, are less likely than single-axis knee users to stub their toes. This benefit can be shared by all transfemoral amputees using four-bar linkage knees. The feature may provide greater confidence for amputees, especially when they are walking on uneven terrain.

Four-bar linkage knees allow for a closer leg-length equality in unilateral transfemoral amputees. The length of the prosthesis often is fabricated to be slightly shorter than the length of the sound leg to aid clearance during swing. However, lower-limb prostheses that are too short have been suspected of causing low back pain. Because of the greater floor clearance afforded by four-bar knees over single-axis knees, the prosthetic length can be made closer to the full length.

Bilateral amputees also benefit from the swing-phase shortening of four-bar linkage knees. The transfemoral/trans tibial amputee normally experiences difficulty with floor clearance during swing phase due to his or her inability to vault and control timing. The bilateral transfemoral amputee frequently resorts to circumduction to clear the floor during swing. Four-bar knees offer obvious benefits for both of these types of problems. Also, with the advent of unique foot/ankle mechanisms that shorten during the stance phase (e.g., the Flex-Foot Vertical Shock Pylon), floor clearance becomes an even more critical issue. Selection of the appropriate knee for this combination of components should include consideration of the shortening characteristics of a multiaxis knee.

After deciding to fit a transfemoral amputee with a four-bar linkage knee, the selection of a particular four-bar knee should be made primarily on the basis of factors other than floor clearance. These other factors include stance-phase stability, swing-phase control, cosmesis, weight of the knee unit, durability and cost.

Conclusion

This article is intended to give practitioners an idea of how four-bar knee mechanisms influence toe clearance. Floor clearance is only one aspect of knee performance; a knee that has more floor clearance than another is not necessarily a "better" knee. All of the fourbar knees tested improved floor clearance compared with single-axis knees, but single-axis knees may still be preferable for some people. Floor clearance typically increased from I to 3 cm for most four-bar linkage knees when compared with a single-axis knee. Clearance increases of this magnitude are considered significant.

Acknowledgements

This work was supported by the National Institute on Disability and Rehabilitation Research, NIDRR grant numbers H133P20016 and H133E30007.

STEVEN A. GARD, PhD, is a postdoctoral fellow of the Northwestern University Prosthetics Research Laboratory & Rehabilitation Engineering Research Program in Chicago.

DUDLEY S. CHILDRESS, PhD, is director of North western University Prosthetics Research Laboratory & Rehabilitation Engineering Research Program, professor of biomedical engineering and orthopaedic surgery at Northwestern University, and executive director of the North western University Prosthetic-Orthotic Center in Chicago.

JACK E. UELLENDAHL, CPO, is director of Prosthetics & Orthotics Clinical Services at the Rehabilitation Institute of Chicago.

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