Roll-over Shape Research Articles

Investigations of roll-over shape: implications for design, alignment, and evaluation of ankle-foot prostheses and orthoses

Purpose. The purpose of this article is to provide an overview of our previous work on roll-over shapes, which are the effective rocker shapes that the lower limb systems conform to during walking.Method. This article is a summary of several recently published articles from the Northwestern University Prosthetics Research Laboratory and Rehabilitation Engineering Research Program on the topic of roll-over shapes. The roll-over shape is a measurement of centre of pressure of the ground reaction force in body-based coordinates. This measurement is interpreted as the effective rocker shape created by lower limb systems during walking.Results. Our studies have shown that roll-over shapes in able-bodied subjects do not change appreciably for conditions of level ground walking, including walking at different speeds, while carrying different amounts of weight, while wearing shoes of different heel heights, or when wearing shoes with different rocker radii. In fact, results suggest that able-bodied humans will actively change their ankle movements to maintain the same roll-over shapes.Conclusions. The consistency of the roll-over shapes to level surface walking conditions has provided insight for design, alignment and evaluation of lower limb prostheses and orthoses. Changes to ankle-foot and knee-ankle-foot roll-over shapes for ramp walking conditions have suggested biomimetic (i.e. mimicking biology) strategies for adaptable ankle-foot prostheses and orthoses.

Effects of prosthetic foot forefoot flexibility on oxygen cost and subjective preference rankings of unilateral transtibial prosthesis users

The investigators conducted a double-blind randomized crossover study to determine the effects of prosthetic foot forefoot flexibility on oxygen cost and subjective preference rankings of 13 unilateral transtibial prosthesis users. Five experimental feet were fabricated for use in the study: F1, F2, F3, F4, and F5. F1 was most flexible, F5 was least flexible, and F3 was designed to conform to a biomimetic ankle-foot roll-over shape. The experimental feet were modeled after the Shape&Roll prosthetic foot (originally produced by Northwestern University, Chicago, Illinois; now in public domain) but had different numbers of saw cuts within the forefoot members, allowing more or less flexibility during walking. Participants walked at the same comfortable, freely selected speed on the treadmill for 7 min with each foot while energy expenditure was measured. No significant difference was found in oxygen cost (mL O(2)/kg/m) between the different feet (p = 0.17), and the order of use was also not significant (p = 0.94). However, the preference ranking was significantly affected by the flexibility of the feet (p = 0.002), with the most flexible foot (F1) ranking significantly poorer than feet F3 (p = 0.003) and F4 (p = 0.004). Users may prefer prosthetic feet that match the flexibility of an intact ankle-foot system, even though we did not detect an energetic benefit at freely selected speeds.

Roll-over shapes of the ankle–foot and knee–ankle–foot systems of able-bodied children

Background The roll-over shape is the effective rocker shape that a lower limb system conforms to during a step. The roll-over shape concept has been explored in detail in adults and has been successfully used in the design, evaluation, and alignment of lower limb prostheses and orthoses. No such analysis exists for the pediatric population. Therefore, the purpose of this study was to investigate the ankle–foot and knee–ankle–foot roll-over shapes in able-bodied children, values that could serve as tools for design and evaluation of lower limb pediatric prostheses and orthoses. Methods This study describes a multi-center retrospective review of existing motion analysis data ( n = 153 from three centers). Roll-over shapes were calculated by transforming center of pressure data from a laboratory-based coordinate system into two body-based coordinate systems. Roll-over shapes were then characterized using a circular arc model. Best-fit radii of roll-over shapes for children in three age groups (3–7 years, 8–11 years, and 12–17 years) were compared using the Kruskal–Wallis test. Findings No significant changes were found in roll-over shape radii between the three age groups ( P = 0.54 for ankle–foot roll-over shape radii; P = 0.12 for knee–ankle–foot roll-over shape radii). The weighted mean of median radii for ankle–foot and knee–ankle–foot roll-over shapes from the three centers were approximately 22% and 17% of body stature, values similar to those seen in adults. Interpretation Children produce nearly circular knee–ankle–foot roll-over shapes at a young age that are similar to those seen in adults when scaled by body stature.

A generic analytical foot rollover model for predicting translational ankle kinematics in gait simulation studies

The objective of this paper is to develop an analytical framework to representing the ankle–foot kinematics by modelling the foot as a rollover rocker, which cannot only be used as a generic tool for general gait simulation but also allows for case-specific modelling if required. Previously, the rollover models used in gait simulation have often been based on specific functions that have usually been of a simple form. In contrast, the analytical model described here is in a general form that the effective foot rollover shape can be represented by any polar function ρ= ρ( φ). Furthermore, a normalized generic foot rollover model has been established based on a normative foot rollover shape dataset of 12 normal healthy subjects. To evaluate model accuracy, the predicted ankle motions and the centre of pressure (CoP) were compared with measurement data for both subject-specific and general cases. The results demonstrated that the ankle joint motions in both vertical and horizontal directions (relative RMSE ∼10%) and CoP (relative RMSE ∼15% for most of the subjects) are accurately predicted over most of the stance phase (from 10% to 90% of stance). However, we found that the foot cannot be very accurately represented by a rollover model just after heel strike (HS) and just before toe off (TO), probably due to shear deformation of foot plantar tissues (ankle motion can occur without any foot rotation). The proposed foot rollover model can be used in both inverse and forward dynamics gait simulation studies and may also find applications in rehabilitation engineering.

Effects of Clinically Prescribed Ankle Foot Orthoses on Ankle-Foot Roll-Over Shapes: A Case Series

ABSTRACT The purpose of this case series was to explore the effects of clinically prescribed ankle-foot orthoses (AFOs) (i.e., the orthosis an individual is provided by their health care team for everyday use) on the ankle-foot roll-over shapes (ROS) of persons with various pathologies. We hypothesized that persons for whom AFOs had been prescribed would have an abnormal ROS and that AFOs would make the ROS similar to that of able-bodied persons. Gait data were recorded from eight adults with unilateral involvement: five subjects (one with a common peroneal nerve injury, one with a subchondral talar cyst, one with an incomplete spinal cord injury, one with hemiplegia due to stroke, and one with postpolio) wore posterior leaf spring AFOs (PLS-AFOs); two subjects (with hemiplegia due to stroke) wore articulated AFOs with a plantar flexion stop and free dorsiflexion; and one subject (with hemiplegia due to stroke) wore a solid AFO. Participants walked with and without their AFO at their freely selected walking speed. “Normal” reference data were recorded from 10 able-bodied subjects of similar age walking at similar speeds. As hypothesized, ROS—as characterized by arc length and arc radius—was abnormal for all subjects when walking without an AFO. However, the prescribed AFOs were only able to partially restore ROS. Arc lengths were closer to normal with the AFO when compared to without, but changes in arc radius were less consistent, with only three subjects having radii that were closer to normal when the AFO was worn. Overall, there were smaller changes in ROS arc length and radius when PLS-AFOs were worn compared with articulated AFOs, consistent with the fact that PLS-AFOs are typically prescribed for those with less severe pathologies. ROS arc length and radius increased in all subjects with stroke when AFOs were worn. The results of this case series suggest that although clinically prescribed AFOs tend to improve ROS compared with walking without an AFO, they do not completely normalize it. Further research is required to assess the relationship between gait dysfunction, AFO design, and ROS.

A Low-Dimensional Sagittal-Plane Forward-Dynamic Model for Asymmetric Gait and Its Application to Study the Gait of Transtibial Prosthesis Users

This paper presents an extension of a recently developed low-dimensional modeling approach for normal human gait to the modeling of asymmetric gait. The asymmetric model is applied to analyze the gait dynamics of a transtibial prosthesis user, specifically the changes in joint torque and joint power costs that occur with variations in sagittal-plane alignment of the prosthesis, mass distribution of the prosthesis, and roll-over shape of the prosthetic foot being used. The model predicts an increase in cost with addition of mass and a more distal location of the mass, as well as the existence of an alignment at which the costs are minimized. The model's predictions also suggest guidelines for the selection of prosthetic feet and suitable alignments. The results agree with clinical observations and results of other gait studies reported in the literature. The model can be a useful analytical tool for more informed design and selection of prosthetic components, and provides a basis for making the alignment process systematic.

Effects of Alignment on the Roll-Over Shapes of Prosthetic Feet

Recent work suggests that a prosthetic ankle-foot component's roll-over shape - the effective rocker it conforms to between initial contact and opposite initial contact (the 'roll-over' interval of walking) - is closely linked to its final alignment in the prosthesis (as determined by a skilled prosthetist using heuristic techniques). If true, this information may help to determine the appropriate alignment for a lower limb prosthesis before it is built, or a priori. Knowledge is needed for future models that will incorporate the roll-over shape including the relative effect of alignment on the roll-over shape's radius of curvature and arc length. The purpose of this study was to evaluate the hypotheses that: (i) Changes in prosthesis alignment alter the position and orientation of a foot's roll-over shape in prosthesis-based coordinates, and (ii) these changes occur without changing the radius of curvature or arc length of the roll-over shape. To examine the hypotheses, this study examined the effects of nine alignment settings on the roll-over shapes of two prosthetic feet. The idea that alignment changes move and rotate roll-over shapes of prosthetic feet in prosthesis coordinates is supported by this work, but the hypothesis that the radius of curvature and arc length do not change for different alignments is not strongly supported by the data. A revised approach is presented that explains some of the changes to the roll-over shape parameters due to changes in rotational alignment.

1P1-B04 圧力中心軌跡の解析に基づく平面足を持つ二足ロボットのリミットサイクル歩行(受動歩行ロボット)

Since most of traditional biped walkers based on Passive Dynamic Walking (PDW) have arc feet and locked ankle joint, they cannot realize multimodal locomotion except walking (e.g. keeping standing posture, running). In this paper, we consider how we can substitute the flat feet with the arc feet. We hypothesize that the arc feet correspond to a circular Roll Over Shape (ROS), which is a shape of trajectory of center of pressure in human walking. We found that this circular ROS was generated by ankle joint driven by flexible muscles antagonistically. Measuring ROS with various tensions of muscles and equilibrium positions of ankle joint, we investigate the relationship between ROS and walking behavior.

Oceanographic Currents and the Convexity of the Uppermost Continental Slope

Immediately below the shelf edge where sea-level lay during the Last Glacial Maximum (LGM), the uppermost continental slope in many areas has a smooth, convex-upwards rounded shape in profile. This shape is an example of a clinoform rollover, a sedimentary feature that arises in general terms from how declining energy with water depth allows sediments to steepen. Computer models using the diffusion transport equation with mobility K declining with depth can produce rollover shapes, but the models have yet to be properly justified and the controls on K have been unclear. In this contribution, aspects of morphologic datasets from the USA and Iberian Atlantic margins are shown to be indeed compatible with the diffusion model. From experiments and theory, the gravity effect on saltating particles leads to a downslope flux that is proportional to local bed gradient, as required by the diffusion model, if the bed is agitated by oscillating currents of small residual current, by contour-parallel currents, or by a combination of both. The predicted mobility K is then an increasing function of the current's average speed. Near-bottom current-meter data reveal how currents, enhanced around the shelf edge, decline with water depth in a way that is generally compatible with the rollover morphology. During the LGM, bed currents due to tides and surface waves were stronger than at present. Although difficult to predict, they are expected to produce a more sharply declining mobility with depth that would be compatible with the limited depth range below the shelf edge over which sand and gravel have deposited.

Summary and Conclusions From the Academy's Eighth State-of-the-Science Conference, on the Biomechanics of Ambulation After Partial Foot Amputation

Summary and Conclusions From the Academy's Eighth State-of-the-Science Conference, on the Biomechanics of Ambulation After Partial Foot Amputation

Roll-over shapes of the able-bodied knee–ankle–foot system during gait initiation, steady-state walking, and gait termination

A few investigators have described the movement of the center of pressure (COP) of the ground reaction force and the activation patterns of the lower limb muscles during gait initiation and termination. This study examines the effective rocker (roll-over shape) behavior of the knee–ankle–foot (KAF) system during gait initiation, steady-state walking (i.e. constant speed gait), and gait termination. The KAF roll-over shapes were characterized by transforming COP data of 10 able-bodied subjects from a laboratory-based coordinate system into a leg-based coordinate system. The resulting roll-over shapes (effective rockers) were characterized using a circular arc model. The KAF roll-over shapes exhibit an overall “flexed” orientation during the first step of gait initiation and an “extended” orientation during the last step of gait termination. Understanding the behavior of the anatomical KAF system during gait initiation and termination may aid in the design of prosthetic components, i.e. mechanical devices that replace complete anatomical structures. Prostheses that intend to mimic the overall behavior of physiological KAF systems (biomimetic designs) could be manufactured using approaches that are much simpler than attempting to reconstruct the complexity of the lower limb.

Effect of ankle-foot orthosis on roll-over shape in adults with hemiplegia

Ankle-foot orthoses (AFOs) are intended to improve toe clearance during swing and ankle position at initial contact (IC) and midstance. Changes that lead to improved ankle-foot kinematics may result in a more biomimetic roll-over shape (ROS). ROS is the effective geometry to which the ankle-foot complex conforms between IC and contralateral IC. An effective ROS during gait may facilitate forward progression. This study investigated the effect of an AFO on ROS in adults with hemiplegia following stroke. Kinematic and force data were recorded from 13 people with hemiplegia and 12 controls. Hemiplegic subjects walked at a self-selected speed with and without an articulated AFO with plantar flexion stop. For the involved limb, the AFO significantly increased the ROS arc length (from 32.6% to 55.7% of foot length [FL]) and arc radius (67.4% to 139.3% of FL) and significantly altered the sagittal plane location of the first center of pressure (COP) point, moving it posterior to the ankle center (-1.2% to -20% of FL) (p < 0.002 for all comparisons). However, when hemiplegic patients walked with an AFO, their mean arc radius was greater, mean arc length less, and the first COP point further posterior than those of control subjects.

The Effects of Prosthetic Foot Roll-Over Shape Arc Length on the Gait of Trans-Tibial Prosthesis Users

The Shape&Roll prosthetic foot was used to examine the effect of roll-over shape arc length on the gait of 14 unilateral trans-tibial prosthesis users. Simple modifications to the prosthetic foot were used to alter the effective forefoot rocker length, leaving factors such as alignment, limb length, and heel and mid-foot characteristics unchanged. Shortening the roll-over shape arc length caused a significant reduction in the maximum external dorsiflexion moment on the prosthetic side at all walking speeds (p < 0.001 for main effect of arc length), due to a reduction in forefoot leverage (moment arm) about the ankle. Roll-over shape arc length significantly affected the initial loading on the sound limb at normal and fast speeds (p = 0.001 for the main effect of arc length), with participants experiencing larger first peaks of vertical ground reaction forces on their sound limbs when using the foot with the shortest effective forefoot rocker arc length. Additionally, the difference between step lengths on the sound and prosthetic limbs was larger with the shortest arc length condition, although this difference was not statistically significant (p = 0.06 for main effect). It appears that prosthesis users may experience a drop-off effect at the end of single limb stance on prosthetic feet with short roll-over shape arc lengths, leading to increased loading and/or a shortened step on the contralateral limb.

Effects on Foot/Ankle Roll-Over Characteristics According to Different Heel Heights during Walking

This study investigated effects on foot/ankle roll-over characteristics according to heel heights during walking. Fifteen female volunteers who have neither musculoskeletal nor foot problems participated in gait analyses, wearing totally four pairs of shoes with different heel heights. To obtain roll-over shape of foot/ankle complex, we used trajectories of ankle, knee and the center of pressure (COP) between initial contact(IC) and opposite initial contact(OIC) to represent as circular arc using the least-square method. We found that the entire roll-over shape moved distally as the heel height increased but roll-over characteristics did not change significantly with different heel heights. In addition, we found that nondisabled persons automatically adapt their foot/ankle complex to changes in heel height shoes up to 6cm, by moving the origin of roll-over shape distally to keep the roll-over characteristics uniform. Roll-over characteristics in human walking would provide a new understanding of human walking, and furthermore can be applied to the design of prosthetics and orthotics of the lower extremity.

Effects of adding weight to the torso on roll-over characteristics of walking

Ten participants without physical impairment walked with 0 kg, 11.5 kg, and 23.0 kg of added weight equally distributed about the torso in a harness. At each weight level, the participants walked at slow, normal, and fast self-selected walking speeds. We examined the roll-over characteristics by determining the ankle-foot and knee-ankle-foot roll-over shapes. These shapes, which are the effective rockers created by the respective lower-limb systems between heel contact and opposite heel contact of walking, are found if one transforms the center of pressure of ground reaction force into body coordinate systems. The roll-over shapes of the ankle-foot and knee-ankle-foot systems did not change appreciably with added weight at any of the three walking speeds. The invariance of these biologic systems to added weight should be considered when prostheses and orthoses are designed that intend to replace and augment their function in walking.

Light emission, chip morphology, and burr formation in drilling the bulk metallic glass

The chip light emission, chip morphology, burr formation and machined surface in drilling of Zr-based bulk metallic glass (BMG) material are investigated. This study demonstrates that the work- and tool-material as well as the feed rate and spindle speed, two drilling process parameters, all affect the onset of chip light emission. Slow feed rate and high spindle speed increase the specific cutting energy and promote the exothermic oxidation and light emission of the chip. Six types of chip morphology, powder, short ribbon, long ribbon, long spiral, long ribbon tangled, and fan, are observed in BMG drilling. The long ribbon tangled chip morphology is unique for BMG material. On the machined surface under quick stop condition, the fracture topography unique to metallic glass with tributary, void, and vein patterns is observed. Different burr formations are observed: the roll-over shape in the entry and the crown shape in the exit edge. The size of burr in the exit edge is typically larger than that in the entrance edge. High feed rate helps to reduce the size of burr in both entrance and exit edges. This study concludes that the WC–Co tool-material, due to its high thermal conductivity and hardness, performs better in drilling BMG than the high speed steel tool.

Roll-over characteristics of human walking on inclined surfaces

Roll-over characteristics of able-bodied human subjects walking on ramped surfaces were examined in this study. Ten subjects walked at their normal self-selected speed on a level surface, a 5-deg ramp, and a 10-deg ramped surface. Ramps were designed such that ground reaction forces and center of pressure of the ground reaction forces could be measured on their surfaces. This set-up facilitated calculation of the effective rockers that the ankle–foot (AF) and knee–ankle–foot (KAF) systems conformed to during single-limb stance (contralateral toe off to contralateral heel contact). Since our original “roll-over shapes” were characterized between heel contact and opposite heel contact, we label the shapes found during single-limb stance as “truncated roll-over shapes”. We hypothesized that the ankle–foot system would adapt to the various surfaces, creating a roll-over shape that would change in orientation with different levels of inclination. The truncated AF roll-over shapes supported this hypothesis for uphill walking but did not support the hypothesis for downhill walking. However, truncated roll-over shapes of the KAF system did adjust their orientation to match both the positive and negative levels of surface inclination. In general, the ankle appears to be the main adapting joint when walking up inclined surfaces while the knee becomes important for the overall adaptation in downhill walking. Knowledge of physiological lower-limb roll-over characteristics on ramped surfaces may help in the development of biomimetic prostheses and orthoses that will automatically adapt to changes in walking surface inclination.

The 'Shape&Roll' Prosthetic Foot: I. Design and Development of Appropriate Technology for Low-Income Countries

The Shape&Roll Prosthetic Foot (patent pending) is an artificial foot designed for use in low-income countries, and may also be useful in industrialised nations. Its design is based on the theory that the roll-over shape of a prosthetic foot should mimic that of the non-disabled physiological foot-ankle complex during walking. This article presents the S&R foot including the unique features incorporated into its design. The results of mechanical tests indicate that the roll-over shape of the foot closely mimics the roll-over shape of the non-disabled ankle-foot complex and an expensive 'high-performance' prosthetic foot. The fatigue testing process for the S&R foot is also described. The foot has been shown to be durable according to the International Organization for Standardization (ISO) standards, with more than five samples tested to date. The Shape&Roll Foot is low in cost, simple to fabricate, light in weight, low in profile, and is highly functional for walking in respect of roll-over characteristics.

Characterisation of prosthetic feet used in low-income countries.

Eleven kinds of prosthetic feet that were designed for use in low-income countries were mechanically characterised in this study. Masses of the different kinds of prosthetic feet varied substantially. Dynamic properties, including damping ratios and resonant frequencies, were obtained from step unloading tests of the feet while interacting with masses comparable to the human body. Data showed that for walking, the feet can be appropriately modeled using their quasistatic properties since natural frequencies were high compared to walking frequencies and since damping ratios were small. Roll-over shapes, the effective rocker (cam) geometries that the feet deform to under walking loads, were determined using a quasistatic loading technique and a spatial transformation of the ground reaction force's centre of pressure. The roll-over shapes for most of the prosthetic feet studied were similar to the roll-over shape of the SACH (solid-ankle cushioned heel) prosthetic foot. All roll-over shapes showed a lack of forefoot support, which may cause a "drop-off" experience at the end of single limb stance and shorter step lengths of the contralateral limb. The roll-over shapes of prosthetic feet appear useful in characterization of foot function.

Roll-over shapes of human locomotor systems: effects of walking speed

Objective. To examine the hypothesis that roll-over shapes of non-disabled lower limb systems do not change appreciably with walking speed. Design. Repeated measures ( n=24). Background. Roll-over shapes of three lower limb systems are presented. They are: roll-over shapes of the (1) foot, (2) ankle–foot, and (3) knee–ankle–foot systems. Roll-over shapes show the effective rocker (or cam) shapes that the lower limb systems conform to during the period in the stance phase of walking between heel contact and opposite heel contact. Methods. Roll-over shapes were measured by transforming center of pressure data from a laboratory-based coordinate system into each of three body-based coordinate systems. Knee–ankle–foot roll-over shapes were further characterized using a circular arc model. Results. From a statistical standpoint, the radii of the best-fit circular arcs did not change significantly with walking speed, while the forward shifts of the circular models did change significantly. However, the change in forward shift was not considered to be clinically significant. Conclusions. The biologic systems involved in developing the roll-over shapes adapt to changing conditions of walking speed, including increased loading amplitudes as speed is increased, to maintain similar effective roll-over geometries. Relevance Roll-over shapes provide insight into the workings of various lower limb systems by taking a new look at existing gait data. This insight could provide broad utility, helping to develop a better understanding of able-bodied and disabled human walking, and leading to the design of improved rehabilitation devices, surgeries, and therapies.