Researchers have identified the roll-over shape as a means of directly measuring rockers during gait. This technique can help determine ways of optimizing orthotic and prosthetic devices so that the resulting gait is as natural as possible.
by Andrew H. Hansen, PhD
Rockers are devices that use their geometry to constrain movement. As an example, a rocking chair has rockers that facilitate a smooth back and forth movement of the chair. Rockers have been used to model functions of the body in walking. Perry described the functions of the human foot and ankle during walking as a series of three rockers: heel, ankle, and forefoot.1 These simple qualitative descriptions have been useful for clinicians to communicate deficiencies in ankle-foot function in persons with disabilities.
Researchers modeling gait have also used rockers to represent the feet and ankle-foot systems.2-6 McGeer5 modeled the ankle-foot system as a circular rocker and successfully created physical models that could walk down gentle slopes using their inherent passive dynamics. Others have followed McGeer’s work, creating more realistic walking machines that utilize rockers and inherent passive dynamics to reduce the amount of energy needed to ambulate.7,8
The rocker is attractive because it simplifies modeling and understanding of complex tasks. But do humans actually use these kinds of rockers in walking? A method developed by Knox9 allows us to answer this question. This article describes our investigations using the roll-over shape, a direct measurement of the effective rockers used by lower limb systems in walking, and the clinical implications of our findings.
The roll-over shape is a measurement that was first described by Erick Knox, a former PhD student of Dudley Childress, PhD, at Northwestern University.9 The technique for determining what Knox termed the “foot shape” was essentially the transformation of the center of pressure of the ground reaction force into a coordinate system based on the lower part of the leg (i.e., the “shank”). Knox even developed a prosthetic foot called the “Shape Foot,” which was a piece of wood cut into the rocker shape that he and Dr. Childress believed to be most favorable for walking. Laboratory subjects walked quite well with the Shape Foot when it had the appropriate radius. Knox left the laboratory after finishing his PhD, and I began at Northwestern University later that year. A good example of being in the right place at the right time, I picked up where Erick had left off and continued this important line of inquiry.
After some early consideration, Dr. Childress and I renamed Knox’s measurement the “ankle-foot roll-over shape,” because it included effects of both the foot and the ankle and because it was the shape that resulted from the roll-over phase of walking. We also developed measurement techniques for other roll-over shapes in the course of our research, including the foot and knee-ankle-foot roll-over shapes.10
The foot, ankle-foot, and knee-ankle-foot roll-over shapes are found by transforming center of pressure positions into foot-, shank-, and leg-based coordinate systems, respectively. As an example, the ankle-foot roll-over shape can be found using markers on the shank of the leg to establish a coordinate system that translates and rotates with the movement of the leg. The center of pressure of the ground reaction force, measured by a force platform, can be transformed into the shank-based coordinate system for each frame of collected data to indicate the ankle-foot roll-over shape. This approach works because the center of pressure provides a location on the floor’s surface where load is applied. With respect to the shank coordinate system, the series of these points during a step represents the effective rocker shape created by the ankle-foot system during the roll-over phase of walking (initial contact to opposite-limb initial contact).
Roll-over shape measurements on able-bodied persons were of great interest to our group because they provided a simple and direct output of complex lower limb systems, namely biomimetic rockers or roll-over shapes. For example, the biomimetic ankle-foot roll-over shape, we believed, could be used to guide the design of prosthetic feet, walking casts, rocker-bottom shoes, and ankle-foot orthoses. It was important to understand the characteristics of the biomimetic roll-over shape and how it was altered when walking at different speeds, carrying added weights, walking with shoes of different heel heights, or walking on non-level terrain. The results of these studies could be used to directly “tune” a device’s roll-over shape for different walking characteristics, allowing the user of the device to more naturally perform all of these activities.
We conducted a study of 24 young able-bodied adults walking at speeds ranging from 0.4 to 2.4 m/s, measuring foot, ankle-foot, and knee-ankle-foot roll-over shapes as a function of speed.10,11 We found generally that the roll-over shape of the foot was flat and that it curled up at the toe break, creating a shape similar to that of a ski. The ankle-foot and knee-ankle-foot roll-over shapes were much different, more closely mimicking a circular rocker shape. In general, the radii of circles fit to the ankle-foot roll-over shapes were variable but did not change appreciably for different walking speeds. The radii of circles fit to the knee-ankle-foot roll-over shapes were less variable but still did not change significantly with walking speed. The median radius of the knee-ankle-foot roll-over shapes from more than 1000 walking trials at different speeds was 16% of the subject’s height, which is about 30% of their leg length (assuming scaling data from Winter12). Interestingly, this value was predicted by McGeer for human walking in the course of his modeling efforts.5 This matching of measurements with McGeer’s prediction supported the idea that people may be using their lower limb systems in a way that exploits natural passive dynamics for low energy walking.
Need vs speed
The finding that knee-ankle-foot roll-over shape radius did not change with walking speed was surprising because higher loads are experienced during fast walking compared with slow walking, yet displacements encountered by the ankle-foot system did not change significantly with walking speed either. This finding suggested that the ankle mechanics were changing at different speeds in order to maintain a consistent roll-over shape. To explore this question, we examined plots of ankle torque versus ankle angle from the same data pool (n = 24 young able-bodied subjects).13 The slopes of these curves suggested impedance values for mechanical replacements of the ankle joint, i.e., the joint’s ability to resist motion when subjected to the forces of gait. In general, we found the loading sections of these curves changed with walking speed, from linear curves at slow speeds to non-linear curves at fast speeds, but all resulting in similar amounts of angular movement at the peak torques. When investigating the loading and unloading portions of the ankle torque versus ankle angle curves, we found that the ankle should be replaceable by a passive system with energy losses at slow speeds, an efficient passive system at normal speeds, and an active system at fast speeds.
Our studies of walking speed showed that fluctuations in forces to the lower limb system did not yield significantly different roll-over shapes. We wondered, though, if more dramatic changes in forces caused by carrying heavy objects would change the roll-over shapes of able-bodied lower limb systems. To investigate this question, we studied 10 young able-bodied subjects, each walking unweighted and with added weights of 25 and 50 pounds distributed evenly about the torso in a harness, and at three self-selected walking speeds.14 We found that the roll-over shapes did not change appreciably with added weight at any of the walking speeds. The invariance of the roll-over shape to both speed and added weight suggested that it could be a goal for the able-bodied lower limb system in walking and that it may be useful for design of lower limb prostheses and orthoses.
In parallel investigations, we examined the effects of shoe heel height on biologic ankle-foot systems15 and prosthetic ankle-foot systems16 for walking and simulated walking respectively. We found that small changes in shoe heel height dramatically changed the orientation of the prosthetic ankle-foot roll-over shape within the shank coordinate system, while much larger changes in shoe heel height did not appreciably change the orientation or radius of the biologic ankle-foot roll-over shape. Also, we found that simple changes in prosthetic alignment could be made to minimize the changes in orientations between roll-over shapes, making the response to shoes of different heel heights more biomimetic. These studies supported the clinical approach of alignment of the prosthetic foot with a shoe and the need for the prosthetic foot’s user to use the same shoes or shoes having the same heel height to avoid “misalignment”. While this knowledge was tacit to many clinicians, the roll-over shape provided some quantitative evidence for this approach.
Studies of walking speed, added weight, and shoe heel height all suggested that able-bodied persons adapt to conditions of level ground walking to maintain an invariant knee-ankle-foot roll-over shape. This finding was powerful in that it suggested lower limb rehabilitation devices intended to replace or augment the lower limb could be designed to conform to this single biomimetic roll-over shape for level walking and to maintain this shape for different walking conditions (see Figure 1).
Using roll-over shape as a goal for design is attractive for level walking because it is not a moving target as opposed to many kinematic or kinetic variables. As an example, the Shape&Roll Prosthetic Foot was designed to conform to the biomimetic ankle-foot roll-over shape and to more-or-less stop deforming at this shape. This behavior was accomplished using cuts in the forefoot section of the Shape&Roll Prosthetic Foot, which created a series of flexural hinges with limited range of motion.17 More work is needed to create a durable cover for the Shape&Roll Prosthetic Foot, but many prosthesis users have commented on the smooth and natural roll-over it provides during walking.
The invariance of the roll-over shape for level walking also supported its use for alignment of transtibial prostheses. In particular, we believed that transtibial alignment was the process of orienting and positioning a prosthetic foot’s roll-over shape to replicate as closely as possible the missing biologic ankle-foot roll-over shape.18 To test this idea, we performed a double-blinded study of seven transtibial amputees using prosthetic feet with largely different roll-over characteristics.19 The study found that, unbeknownst to the certified prosthetist, the clinical process of dynamic alignment nested the various prosthetic foot roll-over shapes (measured in a coordinate system based on the prosthetic socket) toward a single shape. This result supported the idea that prosthetists in fact are aligning prosthetic feet toward one roll-over shape, perhaps the invariant roll-over shape created by biologic ankle-foot systems.
The invariance of roll-over shape also suggested that the measurement could be used as a means to evaluate the biomimesis of current prosthetic and orthotic lower limb systems. One particular variable that appears to be important in the evaluation of prosthetic feet is the physical length of the roll-over shape. Since prosthetic feet are typically used in a heel to toe gait, we created a simple measure extending from the heel of a prosthetic foot to the anterior end of the roll-over shape and termed this measure the “effective foot length” used during a walking step. By dividing this measure by the entire foot length, we created a normalized “effective foot length ratio” (EFLR).20 We measured EFLR values for a number of prosthetic feet used clinically in the 1990s and found a wide range of values, from 0.60 to 0.81. At the same time, our estimate of the EFLR for the biologic ankle-foot system was 0.83.
To investigate the clinical relevance of the EFLR measurement, we ran a study of 14 transtibial prosthesis users walking with prosthetic feet having short, medium, and long effective foot lengths (EFLR values of about 0.6, 0.7, and 0.8 for slow walking). We found that prosthetic feet with short effective foot lengths led the user to “drop-off” the end of the keel in late stance phase (during normal and fast walking speeds), resulting in increased loading to the sound limb.21 These findings helped to explain previous studies that had measured reduced sound limb loading with certain kinds of prosthetic feet compared with others.22,23 Our analyses of prosthetic feet suggested that the findings were likely due to the different EFLR values of the feet used in the studies.
The roll-over shape has also been used to investigate the effectiveness of ankle-foot orthoses.24,25 In these studies, the ankle-foot orthosis restored the heel rocker by providing the heel-to-toe gait normally seen in able-bodied persons. The roll-over shapes in these studies provided quantitative evidence of the heel rocker’s restoration, namely a change in the physical length of the roll-over shape in its posterior section.
While many of our studies have focused on level ground walking, we have also investigated the ankle-foot and knee-ankle-foot roll-over shapes during ramp walking.26 Studying both shapes together suggested that in able-bodied subjects, the ankle is the main adapter when walking uphill and the knee is the main adapter when walking downhill. At this time, there are no lower limb prostheses that can exactly mimic this behavior. However, several ankle-foot systems are becoming commercially available that claim to adapt to different terrain, and several others are in development, including one in our laboratory.27
Investigations of roll-over shape have aided our understanding of walking mechanics and have provided insight for design, alignment, and evaluation of lower limb prostheses and orthoses. The roll-over shape is only one of many important characteristics for lower limb rehabilitation devices. However, we are hopeful that our investigations and future research using this measurement will lead to improved prescriptions and design of rehabilitation devices, as well as subsequent improvements in the lives of their users.
Andrew Hansen, PhD, is a research health scientist at the Minneapolis VA Medical Center in Minneapolis, MN, and an adjunct associate professor of physical medicine and rehabilitation at Northwestern University in Chicago.
Acknowledgements: The author is grateful to the many investigators and research subjects who were involved in the projects described and cited in this paper. In particular, the author would like to thank Dr. Dudley Childress for his mentorship and close collaboration in these studies.
Disclosure: The work described in this paper was supported by grants from the Department of Veterans Affairs, the National Institute on Disability and Rehabilitation Research (NIDRR) of the Department of Education, and a subcontract from the Center for International Rehabilitation (CIR). The opinions expressed in this paper are those of the author and not necessarily those of the funding agencies.
1. Perry, J. Gait analysis: Normal and pathological function. Thorofare, NJ: Slack Incorporated; 1992.
2. Gard SA, Childress DS. What determines the vertical displacement of the body during normal walking? J Prosthet Orthot 2001;13(3):64-67.
3. Ju MS. The modeling and simulation of constrained dynamical systems with application to human gait [PhD thesis]. Cleveland: Case Western Reserve University; 1986.
4. Koopman HFJM. The three-dimensional analysis and prediction of human walking [PhD thesis]. Enschede, The Netherlands: University of Twente;1989.
5. McGeer T. Passive dynamic walking. Int J Robotics Res 1990;9(2):62-82.
6. Morawski J, Wojcieszak I. Miniwalker – a resonant model of human locomotion. In: Asmussen E, Jorgensen K, eds. Biomechanics VIA Int. series on biomechanics. Vol 2A. Baltimore: University Park Press;1978: 445-451.
7. Collins S, Ruina A, Tedrake R, Wisse M. Efficient bipedal robots based on passive-dynamic walkers. Science 2005;307(5712):1082-1085.
8. Collins SH, Wisse M, Ruina A. A three-dimensional passive-dynamic walking robot with two legs and knees. Int J Robotics Res 2001;20(7):607-615.
9. Knox EH. The role of prosthetic feet in walking [PhD thesis]. Evanston, IL: Northwestern University;1996.
10. Hansen AH, Childress DS, Knox EH. Roll-over shapes of human locomotor systems: effects of walking speed. Clin Biomech 2004;19(4):407-414.
11. Hansen, A.H. Roll-over Characteristics of Human Walking With Applications for Artificial Limbs. PhD Thesis, Northwestern University: Evanston
12. Winter, D.A. Biomechanics and motor control of human movement. New York: Wiley; 1990.
13. Hansen AH, Childress DH, Miff SC, et al. The human ankle during walking: implications for design of biomimetic ankle prostheses. J Biomech 2004;37(10):1467-1474.
14. Hansen AH, Childress DS. Effects of adding weight to the torso on roll-over characteristics of walking. J Rehabil Res Dev 2005;42(3):381-390.
15. Hansen AH, Childress DS. Effects of shoe heel height on biologic rollover characteristics during walking. J Rehabil Res Dev 2004;41(4):547-554.
16. Hansen AH, Childress DS. Effects of shoe heel height on the roll-over shapes of prosthetic ankle-foot systems: implications for heel-height adjustable components. J Prosthet Orthot 2009;21(1):48-54.
17. Sam M, Childress DS, Hansen AH, et al. The ‘shape&roll’ prosthetic foot: I. Design and development of appropriate technology for low-income countries. Med Confl Surviv 2004;20(4):294-306.
18. Hansen AH, Childress DS, Knox EH. Prosthetic foot roll-over shapes with implications for alignment of trans-tibial prostheses. Prosthet Orthot Int 2000;24(3):205-215.
19. Hansen AH, Meier MR, Sam M, et al. Alignment of trans-tibial prostheses based on roll-over shape principles. Prosthet Orthot Int 2003;27(2):89-99.
20. Hansen AH, Sam M, Childress DS. The effective foot length ratio (EFLR): A potential tool for characterization and evaluation of prosthetic feet. J Prosthet Orthot 2004;16(2):41-45.
21. Hansen AH, Meier MR, Sessoms PH, Childress DS. The effects of prosthetic foot roll-over shape arc length on the gait of trans-tibial prosthesis users. Prosthet Orthot Int 2006;30(3):286-299.
22. Powers CM, Torburn L, Perry J, Ayyappa E. Influence of prosthetic foot design on sound limb loading in adults with unilateral below-knee amputations. Arch Phys Med Rehabil 1994;75(7):825-829.
23. Snyder RD, Powers CM, Fontaine C, Perry J. The effect of five prosthetic feet on the gait and loading of the sound limb in dysvascular below-knee amputees. J Rehabil Res Dev 1995;32(4):309-315.
24. Fatone S, Hansen AH. Effect of ankle-foot orthosis on roll-over shape in adults with hemiplegia. J Rehabil Res Dev 2007;44(1):11-20.
25. Fatone S, Sorci E, Hansen A. Effects of clinically prescribed ankle foot orthoses on ankle-foot roll-over shapes: a case series. J Prosthet Orthot 2009;21(4):196-203.
26. Hansen AH, Childress DS, Miff SC. Roll-over characteristics of human walking on inclined surfaces. Hum Mov Sci 2004;23(6):807-821.
27. Williams RJ, Hansen AH, Gard SA. Prosthetic ankle-foot mechanism capable of automatic adaptation to the walking surface. J Biomech Eng 2009;131(3):035002.