Four Bar Linkage Knee Analysis by Michael P. Greene, B.S., M.E., C.P.O. INTRODUCTION learn comparative methods of evaluating the efficiency of a particular four bar de­ Modern prosthetists have a wide selec­ sign in attaining its specific mechanical or tion of prosthetic knees to fulfill many in­ cosmetic goals. This skill is extremely im­ dividual specifications. The names "fric­ portant since each four bar design is tion," "safety," "lock," "hydraulic," etc. unique in its operation. Specifically, each quickly recall particular classes of single four bar knee has been designed to en­ axis knees. For these single axis knees, the hance individual characteristics such as name (friction, safety, etc.) simply states a safety, cosmesis, energy conservation unique feature which defines the major and/or swing phase motion. mechanical advantage of that class of knees. Polycentric knees, however, may pre­ sent the prosthetist with confusion. This DEFINITION OF TERMS confusion results from the fact that the 1. Translation or translational motion is term "polycentric" does not define any the movement of a machine element along specific function. Secondly, these knees a straight line. require more than a simple knowledge of 2. Rotation or rotational motion is the mechanics to fully understand their func­ movement of one element of a mechanism tions. about a pivot point. This paper will examine one category of 3. Center of Rotation is the point about polycentric knees which are known as which rotational motion occurs. This may "four bar linkages." Simple methods for be an actual mechanical pivot point on the evaluating these knees will be presented. mechanism or a purely hypothetical point These evaluating methods will enable which may or may not actually be on the the prosthetist to determine the major mechanism. mechanical or cosmetic advantage of most 4. Single Axis Knee—Any knee in which four bar designs. The prosthetist will also the shin moves in pure rotation about a constant center of rotation located at the be a pair of parallel links acting together. knee bolt. However, for mechanical purposes these 5. Polycentric Knee—Any knee whose pairs are considered as single links.) design allows the shin to move in a com­ Fig. 1A is a typical four bar linkage bination of rotational and translational knee. The thigh is considered as a link or motion. At any given instant of time, this bar joining points B and E. This link is combination can be mechanically de­ defined BE. The shin is considered as a scribed as a purely rotational motion link joining points C and D. This link is about a constantly changing center or ro­ called CD. Link BC and ED join the shin to tation known as the instantaneous center the thigh. Together, all four links join at of rotation. four points to complete the four bar link­ 6. Instantaneous Center of Rotation (or age. Fig. IB is a kinematic schematic rep­ Instant Center)—The point about which a resentation of the knee seen in Fig. 1A particular element (shin) may be assumed which shows this typical link arrange­ to be moving in pure rotation at any given ment. instant of motion being analyzed. For a single axis knee this will be a constant point at the knee bolt center. For a polycentric knee this will be a theoretical STABILITY IN STANCE point in the plane of motion (sagittal PHASE OF A FOUR BAR plane). LINKAGE KNEE 7. Four Bar Linkage Knee—A specific class of polycentric knees. The knees are Alpha (a) Stability—At this point it characterized by four elements joined at is assumed that the reader understands four separate points. The four elements the basic theory of the T.K.A. (Trochanter-Knee-Ankle) line and the accepted include the thigh, shin and two links. T.K.A. alignment method of simple single (Note: In actual practice, a single link may axis knee mechanisms. In this method the the equivalent single axis knee will also knee is made more stable (safer) by mov­ be different for each position of flexion. ing the knee center posterior to the T.A. Therefore, care must be taken to analyze (Trochanter-Ankle) line. Conversely, the four bar mechanism at the exact angu­ moving the knee center anterior to the lar position which is in question. T.A. line decreases weight bearing sta­ A simple method of estimating the in­ bility. stantaneous center of rotation of an actual Stability of a four bar knee system is four bar knee mechanism would be to lay also determined by using the T.K.A. two straightedges along the links and note theory. The knee center becomes the the point of intersection. A third straight­ theoretical "instantaneous center of rota­ edge could be aligned with the trochanter tion" in this case. This point must be de­ and ankle center to simulate the T.A. line. termined for each position of the knee Stability of the system is estimated by which is in question. measuring the distance from the T.A. line For static (bench) alignment purposes, to the instant center. For the sake of this the accepted knee position is that of full discussion, this distance will be defined extension. With the knee fully extended as "a" (alpha). A positive a value is de­ the instantaneous center for rotation is fined as a knee center which is posterior to determined by drawing a line through the T.A. line. This is a stable or "positive a each of the two links joining the shin to stability" condition. A negative a value the thigh (see Fig. 1A). The instantaneous indicates an unstable system with the center of rotation (point O) is the point knee center anterior to the T.A. line. where these two lines intersect. The sta­ At this point it is interesting to compare bility of the system is determined by not­ a prosthesis with a single axis knee to the ing the position of this instant center in four bar knee prosthesis seen in Fig. 1A. relation to the T.A. line. As in the single The single axis knee has an a = 0 value at axis knee, the center of rotation must be posterior to the T.A. line to be considered as a stable weight bearing system. At this point the reader's understanding of the "instantaneous center of rotation" and of four bar knee motion may be un­ clear; this confusion can be eliminated if one understands that a four bar knee is mechanically equivalent to a particular hypothetical single axis knee at any in­ stant of motion being analyzed. This hy­ pothetical knee has its knee bolt located at the instant center of the equivalent four bar knee. Fig.lC gives the single axis equivalent of the four bar knee depicted in Fig. 1A (at the full extension position only). Therefore, the motion and mech­ anical reaction of the four bar knee in Fig. 1A is precisely identical to that of the single axis knee seen in Fig. 1C at this position of extension. Often it is easier to understand the reaction of the four bar if one visualizes this instantaneous single axis equivalent rather than the actual four bar mechanism. Since the instant center of a four bar is changing through each position of flexion, Fig. L-C full extension. As it begins to flex, a be­ nent of load applied at the knee bolt by the comes negative and progressively more thigh section. The force E is the force unstable as flexion continues. The special applied to extend the knee mechanism. four bar knee in Fig. 1A has a positive a This force is also applied by the thigh at value at full extension. As flexion begins, the knee bolt. Forces Rv and Rh are the the value becomes smaller but it remains vertical and horizontal components of the positive for the first few degrees of flexion. floor reaction force. To analyze this situa­ Obviously, this knee was designed to tion, moments are summed to equal zero have enchanced stance stability and about the point "f" to yield the equation: therefore could accurately be called a "four bar safety knee." It is noted that if the knee center is raised, Beta (B) Stability—A second and the value of "y" and of L will remain un­ unique condition affecting knee stability changed. However, the value of "h" will exists with all four bar knee mechanisms. increase and for the above equation to Referring to Fig. 1A, it is noted that the balance; the value of E will proportion­ instantaneous center of rotation is super­ ately decrease. This simply means that the ior to the level of the mechanical (or cos­ moment tending to cause knee buckling is metic) knee center (point Kc). With this reduced and therefore the patient uses less prosthetic knee the patient gains a force, E, to hold the knee in extension. mechanical advantage over a typical single The second way in which knee stability axis knee. This mechanical advantage is is increased by raising the knee center is gained in two ways as a result of raising demonstrated in Fig. 2B. This represents a the instant center. typical above knee prosthetic thigh. Force Fig. 2A is a free body diagram of a typi­ W and I are the loads applied to socket by cal above knee prosthetic shin shortly after the patient, (note: W and I are assumed to heel strike. The force L is the axial compo­ act on a point along the T.K.A. for this analysis.