Coding proprioceptive information to control movement to a target: Simulation with a simple neural network

When the stick insect walks, the middle and rear legs step to positions immediately behind the tarsus of the adjacent rostral leg. Previous reports have described this movement to a target as a relationship between the tarsus positions of the two legs in a Cartesian coordinate system. However, leg proprioceptors measure the position of the target leg in terms of joint angles and leg muscles bring the tarsus of the moving leg to the proper end-point by establishing appropriate angles at the joints. Representation of this task in Cartesian coordinates requires non-linear coordinate transformations; realizing such a transformation in the nervous system appears to require many neurons. The present simulation using the back-propagation algorithm shows that a simple network of only nine units — 3 sensory input units, 3 motor output units, and 3 hidden units — suffices. The simulation also shows that an analytic coordinate transformation can be replaced by a direct association of joint configurations in the moving leg with those in the target leg.     

MMG and EMG responses of the superficial quadriceps femoris muscles.

Eighteen adults performed isometric muscle actions of the leg extensors at 25, 50, 75, and 100% maximal voluntary contraction (%MVC) at leg flexion angles of 25, 50, and 75 degrees. The results indicated that isometric torque production increased as leg flexion angle increased (75 degrees > 50 degrees > 25 degrees). For each muscle tested (rectus femoris, vastus lateralis, and vastus medialis), the EMG amplitude increased up to 100%MVC at each leg flexion angle (25, 50, and 75 degrees). The MMG amplitude for each muscle, however, increased up to 100%MVC at 25 and 50 degrees of leg flexion, but plateaued from 75 to 100%MVC at 75 degrees of leg flexion. We hypothesize that the varied patterns for the MMG amplitude-isometric torque relationships were due to leg flexion angle differences in: (1) muscle stiffness, (2) intramuscular fluid pressure, or (3) motor unit firing frequency.     

Fatigue-related changes in motor-unit synchronization of quadriceps muscles within and across legs

Two experiments were conducted to examine effects of muscle fatigue on motor-unit synchronization of quadriceps muscles (rectus femoris, vastus medialis, vastus lateralis) within and between legs. We expected muscle fatigue to result in an increased common drive to different motor units of synergists within a leg and, hence, to increased synchronization, i.e., an increased coherence between corresponding surface EMGs. We further expected fatigue-related motor overflow to cause motor-unit synchronization of homologous muscles of both legs, although to a lesser extent than for synergists within a leg. In the first experiment, different levels of fatigue were induced by varying posture (knee angle), whereas in the second experiment fatigue was induced in a fixed posture by instructing participants to produce different force levels. EMG coherence was found in two distinct frequency bands (6–11 and 13–18 Hz) and was higher within a leg than between legs. The fatigue-related increase of 6–11 Hz inter-limb synchronization resembled the increased motor overflow during unimanual contractions and thus hinted at an increase in bilateral coupling. Synchronization at 13–18 Hz was clearly different and appeared to be related to posture.     

LANDING QUALITY IN ARTISTIC GYMNASTICS IS RELATED TO LANDING SYMMETRY

In gymnastics every exercise finishes with a landing. The quality of landing depends on subjective (e.g. biomechanical) and objective (e.g. mechanical characteristics of landing area) factors. The aim of our research was to determine which biomechanical (temporal, kinematic and dynamic) characteristics of landing best predict the quality of landing. Twelve male gymnasts performed a stretched forward and backward salto; also with 1/2, 1/1 and 3/2 turns. Stepwise multiple regression extracted five predictors which explained 51.5% of landing quality variance. All predictors were defining asymmetries between legs (velocities, angles). To avoid asymmetric landings, gymnasts need to develop enough height; they need higher angular momentum around the transverse and longitudinal axis and they need to better control angular velocity in the longitudinal axis.     

The impact of seatback angle on electromyographical activity of the lower back and quadriceps muscles during bilateral knee extension

This study investigated variations in electromyographic (EMG) responses of the erector spinae (ES), vastus medialis (VM), rectus femoris (RF), and vastus lateralis (VL) to different seatback angles during leg extension. Twenty men and women (10 men, 10 women; age 27.49 +/- 6.16 years) performed 8 repetitions at 70% of 8 repetition maximum at seatback angles of 1.57, 1.75, and 1.92 radius (rad). Analyses using repeated-measures analysis of variance indicated the greatest root square mean of the EMG (rmsEMG) and integrated EMG (intEMG) for the ES were at 1.92 rad, and the greatest for the VM (concentric) and VL (eccentric) were at 1.57 rad. No differences were observed among seat angles for the RF except for a higher normalized intEMG at 1.92 than 1.75 rad (concentric). Throughout all sets for all conditions and muscles, rmsEMG and intEMG significantly increased and median power frequency significantly decreased. These data indicate that a seatback angle of 1.57 rad is best for a leg extension machine, because this angle maximizes quadriceps activity while minimizing stress on the lower back muscles.     

Biomimetic Design and Optimal Swing of a Hexapod Robot Leg

Biological inspiration has spawned a wealth of solutions to both mechanical design and control schemes in the efforts to develop agile legged machines. This paper presents a compliant leg mechanism for a small six-legged robot, HITCR-ll, based on abstracted anatomy from insect legs. Kinematic structure, relative proportion of leg segment lengths and actuation system were analyzed in consideration of anatomical structure as well as muscle system of insect legs and desired mobility. A spring based passive compliance mechanism inspired by musculoskeletal structures of biological systems was integrated into distal segment of the leg to soften foot impact on touchdown. In addition, an efficient locomotion planner capable of generating natural movements for the legs during swing phase was proposed. The problem of leg swing was formulated as an optimal control procedure that satisfies a series of locomotion task terms while minimizing a biologically-based objective function, which was solved by a Gauss Pseudospectral Method （GPM） based numerical technique. We applied this swing generation algorithm to both a simulation platform and a robot prototype. Results show that the proposed leg structure and swing planner are able to successfully perform effective swing movements on rugged terrains.     

Comparative Study on Biomechanics of Two Legs in the Action of Single-Leg Landing in Men’s Badminton

This study aims to analyze the biomechanical difference between the two legs of male badminton players when they land on one leg, thereby providing some guidance for preventing sports injury. Ten male badminton players were selected as the subjects. They did the single-leg landing movement successfully three times. The kinematic data were obtained by the Vicon infrared high-speed motion capture system. The kinetic data were obtained by the KISTLER three-dimensional forcing measuring platform. The data were processed and analyzed. The center of gravity of the right leg on the X and Y axes were 0.25 ± 0.05 and 0.21 ± 0.04 m, respectively, which were lower than that of the left leg (p < 0.05). At the moment of landing by a single leg, the hip angle of the left and right legs was 164.78 ± 6.12° and 156.29 ± 6.89°, respectively (p < 0.05), the hip joint speed of the left and right legs was 2.21 ± 0.32 and 1.98 ± 0.31 m/s, respectively (p < 0.05), the knee joint speed of the left and right legs was 2.51 ± 0.21 and 2.21 ± 0.21 m/s, respectively (p < 0.05). Although there was no significant difference in the range of joint motion, the motion range of the right leg was larger than that of the left leg, and the buffering time of the knee joint of the right leg was also significantly less than that of the left leg. The comparison of the kinetic data demonstrated that the ground reaction force (GRF), peak vertical ground reaction force (PVGRF), and lower limb stiffness of the right leg were significantly smaller than those of the left leg, and the time to peak force was greater than that of the left leg (p < 0.05). The injury risk of the left leg is greater than that of the right leg when the athlete land on a single leg. In the process of training, the athlete should strengthen the stability training of two legs, especially the left leg, in order to reduce sports injury.     

Energy absorption as a predictor of leg impedance in highly trained females

Although leg spring stiffness represents active muscular recruitment of the lower extremity during dynamic tasks such as hopping and running, the joint-specific characteristics comprising the damping portion of this measure, leg impedance, are uncertain. The purpose of this investigation was to assess the relationship between leg impedance and energy absorption at the ankle, knee, and hip during early (impact) and late (stabilization) phases of landing. Twenty highly trained female dancers (age = 20.3 +/- 1.4 years, height = 163.7 +/- 6.0 cm, mass = 62.1 +/- 8.1 kg) were instrumented for biomechanical analysis. Subjects performed three sets of double-leg landings from under preferred, stiff, and soft landing conditions. A stepwise linear regression analysis revealed that ankle and knee energy absorption at impact, and knee and hip energy absorption during the stabilization phases of landing explained 75.5% of the variance in leg impedance. The primary predictor of leg impedance was knee energy absorption during the stabilization phase, independently accounting for 55% of the variance. Future validation studies applying this regression model to other groups of individuals are warranted.     

Reduced knee joint moment in ACL deficient patients at a cost of dynamic stability during landing

The current study aimed to examine the effect of anterior cruciate ligament deficiency (ACLd) on joint kinetics and dynamic stability control after a single leg hop test (SLHT). Twelve unilateral ACLd patients and a control subject group (n=13) performed a SLHT over a given distance with both legs. The calculation of joint kinetics was done by means of a soft-tissue artifact optimized rigid full-body model. Margin of stability (MoS) was quantified by the difference between the base of support and the extrapolated center of mass. During landing, the ACLd leg showed lower external knee flexion moments but demonstrated higher moments at the ankle and hip compared to controls (p<0.05). The main reason for the joint moment redistribution in the ACLd leg was a more anterior position of the ground reaction force (GRF) vector, which affected the moment arms of the GRF acting about the joints (p<0.05). For the ACLd leg, trunk angle was more flexed over the entire landing phase compared to controls (p<0.05) and we found a significant correlation between moment arms at the knee joint and trunk angle (r2 = 0.48;p<0.01). The consequence of this altered landing strategy in ACLd legs was a more anterior position of the center of mass reducing the MoS (p<0.05). The results illustrate the interaction between trunk angle, joint kinetics and dynamic stability during landing maneuvers and provide evidence of a feedforward adaptive adjustment in ACLd patients (i.e. more flexed trunk angle) aimed at reducing knee joint moments at the cost of dynamic stability control.     

Improving horizontal plane locomotion via leg angle control

The lateral leg spring model has been shown to accurately represent horizontal plane locomotion characteristics of sprawled posture insects such as the cockroach Blaberus discoidalis. While passively stable periodic gaits result from employing a constant leg touch-down angle for this model, utilizing a similar protocol for a point mass model of locomotion in three dimensions produces only unstable periodic gaits. In this work, we return to the horizontal plane model and develop a simple control law that prescribes variations in the leg touch-down angle in response to external perturbations. The resulting control law applies control once per stance phase, at the instant of leg touch-down, and depends upon previous leg angles defined in the body reference frame. As a result, our control action is consistent with the neural activity evidenced by B. discoidalis during locomotion over flat and rough terrain, and utilizes variables easily sensed by insect mechanoreceptors. Application of control in the lateral leg spring model is shown to improve stability of periodic gaits, enable stabilization of previously unstable periodic gaits, and maintain or improve the basin of stability of periodic gaits. The magnitude of leg touch-down angle variations utilized during stabilization appear consistent with the natural variations evidenced by single legs during locomotion over flat terrain.     

Kinematics of walking in the hermit crab,Pagurus pollicarus

Hermit crabs are decapod crustaceans that have adapted to life in gastropod shells. Among their adaptations are modifications to their thoracic appendages or pereopods. The 4th and 5th pairs are adapted for shell support; walking is performed with the 2nd and 3rd pereopods, with an alternation of diagonal pairs. During stance, the walking legs are rotated backwards in the pitch plane. Two patterns of walking were studied to compare them with walking patterns described for other decapods, a lateral gait, similar to that in many brachyurans, and a forward gait resembling macruran walking.Video sequences of free walking and restrained animals were used to obtain leg segment positions from which joint angles were calculated. Leading legs in a lateral walk generated a power stroke by flexion of MC and PD joints; CB angles often did not change during slow walks. Trailing legs exhibited extension of MC and PD with a slight levation of CB. The two joints, B/IM and CP, are aligned at 90° angles to CB, MC and PD, moving dorso-anteriorly during swing and ventro-posteriorly during stance. A forward step was more complex; during swing the leg was rotated forward (yaw) and vertically (pitch), due to the action of TC. At the beginning of stance, TC started to rotate posteriorly and laterally, CB was depressed, and MC flexed. As stance progressed and the leg was directed laterally, PD and MC extended, so that at the end of stance the dactyl tip was quite posterior. During walks of the animal out of its shell, the legs were extended more anterior-laterally and the animal often toppled over, indicating that during walking in a shell its weight stabilized the animal.An open chain kinematic model in which each segment was approximated as a rectangular solid, the dimensions of which were derived from measurements on animals, was developed to estimate the CM of the animal under different load conditions. CM was normally quite anterior; removal of the chelipeds shifted it caudally. Application of forces simulating the weight of the shell on the 5th pereopods moved CM just anterior to the thoracic-abdominal junction. However, lateral and vertical coordinates were not altered under these different load conditions. The interaction of the shell aperture with proximal leg joints and with the CM indicates that the oblique angles of the legs, due primarily to the rotation of the TC joints, is an adaptation that confers stability during walking.     

Rectifying postures reconstructed from joint angles to meet constraints.

Postures are often described and modeled using angles between body segments rather than joint coordinates. Models can be used to predict these angles as a function of anthropometry and postural requirements. Postural representation, however, requires the joint coordinates. The use of conventional forward kinematics to derive joint coordinates from predicted angles may violate task constraints, such as the placement of a hand on a target or a foot on a pedal. Errors arise because the anthropometry or other motion characteristics of a subject, for which the prediction is to be made, may differ from the data from which the prediction model was derived. We describe how to rectify model-predicted postures to exactly satisfy such task constraints. We require that the model used for predicting the angles also produce estimates of the variation in these predictions. We show how to alter the initial angle predictions, with the amount of perturbation at each angle dependent on the accuracy of its estimation, so as to exactly satisfy the joint coordinate constraints. Finally, we show in an empirical example that this correction usually produces better overall predictions of posture than those obtained initially.     

Three-dimensional measurement of rearfoot motion during running

Excessive ranges of motion during running have been speculated to be connected to injuries to the lower extremities. Movement of the foot and lower leg has commonly been studied with two-dimensional techniques. However, differences in the alignment of the longitudinal axis of the foot with the camera axis will produce measurement errors for projected angles of the lower extremities. A three-dimensional approach would not have this limitation. The purpose of this study is to present a three-dimensional model for calculation of angles between lower leg and foot, lower leg and ground, and foot and ground, and to compare results from treadmill running derived from this model with results derived from a two-dimensional model for different alignment angles between foot axis and camera axis. A two camera Selspot system was used to obtain three-dimensional information on motion of the studied segments. It was found that several two-dimensional variables measured from a posterior view are very sensitive to the alignment angle between the foot and the camera axis. Some variables change as much as 1 degrees for every 2 degrees of change of the alignment angle. The large influence of rotations other than the measured one in two-dimensional measurements makes advisable the use of a three-dimensional model when studying motion between foot and lower leg during running.     

Common motor mechanisms support body load in serially homologous legs of cockroaches in posture and walking

We studied the mechanisms underlying support of body load in posture and walking in serially homologous legs of cockroaches. Activities of the trochanteral extensor muscle in the front or middle legs were recorded neurographically while animals were videotaped. Body load was increased via magnets attached to the thorax and varied through a coil below the substrate. In posture, tonic firing of the slow trochanteral extensor motoneuron (Ds) in each leg was strongly modulated by changing body load. Rapid load increases produced decreases in body height and sharp increments in extensor firing. The peak of extensor activity more closely approximated the maximum velocity of body displacement than the body position. In walking, extensor bursts in front and middle legs were initiated during swing and continued into the stance phase. Moderate tonic increases in body load elicited similar, specific, phase dependent changes in both legs: extensor firing was not altered in swing but was higher after foot placement in stance. These motor adjustments to load are not anticipatory but apparently depend upon sensory feedback. These data are consistent with previous findings in the hind legs and support the idea that body load is countered by common motor mechanisms in serially homologous legs.     

Knee and Hip Joint Kinematics Predict Quadriceps and Hamstrings Neuromuscular Activation Patterns in Drop Jump Landings

PurposeThe purpose was to assess if variation in sagittal plane landing kinematics is associated with variation in neuromuscular activation patterns of the quadriceps-hamstrings muscle groups during drop vertical jumps (DVJ).MethodsFifty female athletes performed three DVJ. The relationship between peak knee and hip flexion angles and the amplitude of four EMG vectors was investigated with trajectory-level canonical correlation analyses over the entire time period of the landing phase. EMG vectors consisted of the {vastus medialis(VM),vastus lateralis(VL)}, {vastus medialis(VM),hamstring medialis(HM)}, {hamstring medialis(HM),hamstring lateralis(HL)} and the {vastus lateralis(VL),hamstring lateralis(HL)}. To estimate the contribution of each individual muscle, linear regressions were also conducted using one-dimensional statistical parametric mapping.ResultsThe peak knee flexion angle was significantly positively associated with the amplitudes of the {VM,HM} and {HM,HL} during the preparatory and initial contact phase and with the {VL,HL} vector during the peak loading phase (p<0.05). Small peak knee flexion angles were significantly associated with higher HM amplitudes during the preparatory and initial contact phase (p<0.001). The amplitudes of the {VM,VL} and {VL,HL} were significantly positively associated with the peak hip flexion angle during the peak loading phase (p<0.05). Small peak hip flexion angles were significantly associated with higher VL amplitudes during the peak loading phase (p = 0.001). Higher external knee abduction and flexion moments were found in participants landing with less flexed knee and hip joints (p<0.001).ConclusionThis study demonstrated clear associations between neuromuscular activation patterns and landing kinematics in the sagittal plane during specific parts of the landing. These findings have indicated that an erect landing pattern, characterized by less hip and knee flexion, was significantly associated with an increased medial and posterior neuromuscular activation (dominant hamstrings medialis activity) during the preparatory and initial contact phase and an increased lateral neuromuscular activation (dominant vastus lateralis activity) during the peak loading phase.     

Stable operation of an elastic three-segment leg

Quasi-elastic operation of joints in multi-segmented systems as they occur in the legs of humans, animals, and robots requires a careful tuning of leg properties and geometry if catastrophic counteracting operation of the joints is to be avoided. A simple three-segment model has been used to investigate the segmental organization of the leg during repulsive tasks like human running and jumping. The effective operation of the muscles crossing the knee and ankle joints is described in terms of rotational springs. The following issues were addressed in this study: (1) how can the joint torques be controlled to result in a spring-like leg operation? (2) how can rotational stiffnesses be adjusted to leg-segment geometry? and (3) to what extend can unequal segment lengths and orientations be advantageous? It was found that: (1) the three-segment leg tends to become unstable at a certain amount of bending expressed by a counterrotation of the joints; (2) homogeneous bending requires adaptation of the rotational stiffnesses to the outer segment lengths; (3) nonlinear joint torque-displacement behaviour extends the range of stable leg bending and may result in an almost constant leg stiffness; (4) biarticular structures (like human gastrocnemius muscle) and geometrical constraints (like heel strike) support homogeneous bending in both joints; (5) unequal segment lengths enable homogeneous bending if asymmetric nominal angles meet the asymmetry in leg geometry; and (6) a short foot supports the elastic control of almost stretched knee positions. Furthermore, general leg design strategies for animals and robots are discussed with respect to the range of safe leg operation.     

The impact of foot position on electromyographical activity of the superficial quadriceps muscles during leg extension

This study investigated variations in electromyographic (EMG) responses of the vastus lateralis (VL), rectus femoris (RF), and vastus medialis (VM) due to foot position during leg extension. Twenty-four men and women (23.67 +/= 4.02 years) performed 8 repetitions at 70% of 8 repetition maximum with their leg medially rotated, laterally rotated, and neutral. Repeated-measures analyses of variance indicated that the highest normalized root mean square (NrmsEMG) for the VM and VL occurred with medial rotation, and the highest NrmsEMG for the RF occurred with lateral rotation. Significant NrmsEMG increases and median power frequency decreases occurred across repetitions regardless of foot position. Therefore, medial rotation produced the greatest muscle activation for the VL and VM, whereas lateral rotation produced the greatest activation in the RF. These findings are applicable to athletes or bodybuilders who are seeking to selectively increase either the size or performance of a specific muscle of the quadriceps group.     

Leg kinematics and muscle activity during treadmill running in the cockroach, Blaberus discoidalis : I. Slow running

We have combined high-speed video motion analysis of leg movements with electromyogram (EMG) recordings from leg muscles in cockroaches running on a treadmill. The mesothoracic (T2) and metathoracic (T3) legs have different kinematics. While in each leg the coxa-femur (CF) joint moves in unison with the femur-tibia (FT) joint, the relative joint excursions differ between T2 and T3 legs. In T3 legs, the two joints move through approximately the same excursion. In T2 legs, the FT joint moves through a narrower range of angles than the CF joint. In spite of these differences in motion, no differences between the T2 and T3 legs were seen in timing or qualitative patterns of depressor coxa and extensor tibia activity. The average firing frequencies of slow depressor coxa (Ds) and slow extensor tibia (SETi) motor neurons are directly proportional to the average angular velocity of their joints during stance. The average Ds and SETi firing frequency appears to be modulated on a cycle-by-cycle basis to control running speed and orientation. In contrast, while the frequency variations within Ds and SETi bursts were consistent across cycles, the variations within each burst did not parallel variations in the velocity of the relevant joints. Accepted: 24 May 1997     

Evaluating the validity and reliability of inertial measurement units for determining knee and trunk kinematics during athletic landing and cutting movements

Inertial Measurement Units (IMUs) are promising alternatives to laboratory-based motion capture methods in biomechanical assessment of athletic movements. The aim of this study was to investigate the validity of an IMU system for determining knee and trunk kinematics during landing and cutting tasks for clinical and research applications in sporting populations. Twenty-seven participants performed five cutting and landing tasks while being recorded using a gold-standard optoelectronic motion capture system and an IMU system. Intra-class coefficients, Pearson’s r, root-mean-square error (RMSE), bias, and Bland-Altman limits of agreements between the motion capture and IMU systems were quantified for knee and trunk sagittal- and frontal-plane range-of-motion (ROM) and peak angles. Our results indicate that IMU validity was task-, joint-, and plane-dependent. Based on good-to-excellent (ICC) correlation, reasonable accuracy (RMSE < 5°), bias within 2°, and limits of agreements within 10°, we recommend the use of this IMU system for knee sagittal-plane ROM estimations during cutting, trunk sagittal-plane peak angle estimation during the double-leg landing task, trunk sagittal-plane ROM estimation for almost all tasks, and trunk frontal-plane peak angle estimation for the right single-leg landing task. Due to poor comparisons with the optoelectronic system, we do not recommend this IMU system for knee frontal-plane kinematic estimations.     

Training multi-parameter gaits to reduce the knee adduction moment with data-driven models and haptic feedback

The purpose of this study was to evaluate gait retraining for reducing the knee adduction moment. Our primary objective was to determine whether subject-specific altered gaits aimed at reducing the knee adduction moment by 30% or more could be identified and adopted in a single session through haptic (touch) feedback training on multiple kinematic gait parameters. Nine healthy subjects performed gait retraining, in which data-driven models specific to each subject were determined through experimental trials and were used to train novel gaits involving a combination of kinematic changes to the tibia angle, foot progression and trunk sway angles. Wearable haptic devices were used on the back, knee and foot for real-time feedback. All subjects were able to adopt altered gaits requiring simultaneous changes to multiple kinematic parameters and reduced their knee adduction moments by 29-48%. Analysis of single parameter gait training showed that moving the knee medially by increasing tibia angle, increasing trunk sway and toeing in all reduced the first peak of the knee adduction moment with tibia angle changes having the most dramatic effect. These results suggest that individualized data-driven gait retraining may be a viable option for reducing the knee adduction moment as a treatment method for early-stage knee osteoarthritis patients with sufficient sensation, endurance and motor learning capabilities.