Comprehensive Physiology Wiley Online Library

Biomechanical Insights into Neural Control of Movement

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Abstract

The sections in this article are:

1 Analytical Techniques and Terms
1.1 Biomechanics Terminology
1.2 Dynamics Variables
1.3 Single vs. Multiple Degrees of Freedom
1.4 Free‐Body Diagram
1.5 Dynamics Techniques
2 Insights from Inverse Dynamics
2.1 Equations of Motion
2.2 Anthropometric Data
2.3 Predictions Using an Inverse Dynamics Model
3 Control of Different Locomotion Forms
3.1 Swing‐Phase Dynamics
3.2 Stance‐Phase Dynamics
3.3 Insights for Neural Control of Locomotion
4 Role of Dynamics in the Control of Arm Movements
4.1 Limb Postural Dynamics
4.2 Intersegmental Dynamics Change with Practice
5 Changes in Limb Dynamics During Development
5.1 Spontaneous Kicking Behaviors
5.2 Acquisition of Reaching
6 Concluding Remarks
Figure 1. Figure 1.

Nonintuitive relations between torque and kinematics. Data are from a subject pointing forward, moving the hand in the sagittal plane to a target at shoulder level. The joint motions required were shoulder flexion (upward angle trace) and elbow extension (downward angle trace). While these opposite motions occurred, agonists for this action were shoulder flexors (e.g., anterior deltoid) and elbow flexors (e.g., biceps brachii), with shoulder and elbow joint torques that both had increased flexor influences.

Adapted from Fig. of Soechting and Flanders
Figure 2. Figure 2.

Interpretive and free‐body diagrams of a model of an infant's upper extremity. The upper diagram shows the limb positioned in an inertial (x‐y‐z) coordinate system. A positive torque is defined (M). The upper extremity is modeled as three interconnected rigid segments (S1 hand, S2 forearm, and S3 upper arm) with frictionless joints (J1 wrist, J2 elbow, and J3 shoulder). At each instant in time during a reach, a moving local plane (P) is calculated so that the plane contains the x‐y‐z coordinates of each of the three joint centers (J1, J2, J3). The planar torques at the wrist, elbow, and shoulder are calculated with respect to the respective joint axes (Z1', Z2', Z3') that pass through each joint center and are perpendicular to the moving local plane (P). In the lower portion of the figure is a free‐body diagram of the upper extremity. Depicted are forces related to the hand, forearm, and upper arm segment weights (W1, W2, W3) acting at their respective center of mass, and the wrist, elbow, and shoulder joint reaction forces (F1, F2, F3) and torques (M1, M2, M3).

Adapted from Fig. of Zernicke and Schneider
Figure 3. Figure 3.

Anatomical drawing of the cat hindlimb with a schematic of a force platform beneath it. E‐shaped tendon transducers are shown on the lateral gastrocnemius (LG) and tibialis anterior (TA) tendons. FR is the resultant ground reaction force vector acting on the plantar surface of the paw. Each force platform contains two piezoelectric transducers (TR). Digit (θd), tarsal (θt), and shank (θS) segment angles are calculated from the right horizontal. Ma is the muscle torque acting about the ankle joint.

Redrawn from Fig. (a) of Fowler et al.
Figure 4. Figure 4.

Hindlimb coordination for the paw shake. The response is tested with the spinalized cat held vertically; tape is wrapped around the paw (A). Positions at the start of a cycle (A1, peak ankle extension) and mid‐cycle (A2, peak ankle flexion) are shown. Hindlimb segments (thigh, leg, paw) are outlined; each joint (hip, knee, ankle) is marked by a dot. In B, EMG records of four cycles are from an ankle extensor (LG) and flexor (TA); knee extensor (VL) and hip extensor‐knee flexor (BF). Kinematics for four steady‐state cycles are shown in C; 50 ms intervals mark the abscissa. An angle‐angle plot in D illustrates knee‐ankle coordination for steady‐state cycles. Each cycle begins at peak ankle extension (a) and proceeds in a counterclockwise direction. First the knee extends and ankle flexes. Peak knee extension (b) precedes peak ankle flexion. Next, the knee flexes and later the ankle extends (c). Dots on the curve mark time intervals of 5 ms. Bars indicate timing of EMG bursts for LG and BF (stippled), VL (shaded), and TA (unshaded).

Adapted from Figs. and of Smith and Zernicke
Figure 5. Figure 5.

Torque components during a typical paw‐shake cycle. The net, muscle, and motion‐dependent torques are shown for the ankle (top) and knee (bottom) joints. The gravitational torque was negligible at both joints and is not illustrated. At the ankle, the main motion‐related torques (leg angular acceleration and knee linear acceleration) counterbalance each other, and the muscle torque dominated the net torque. Positive values represent flexor torques. At the knee, paw angular acceleration (the main inertial torque) is counterbalanced by muscle torque, and net torque is negligible. Positive values represent extensor torques. Bars show the timing of EMG bursts for extensor and flexor muscles at the ankle and knee. Records are aligned by cycle time; vertical lines mark kinematic events.

Adapted from Figs. A and A of Hoy et al.
Figure 6. Figure 6.

Disruption of knee extensor activity during paw‐shake responses elicited under two conditions. The EMG record in A shows a paw‐shake response with knee and ankle joint immobilized by a plaster cast, while the record in B shows a response with a flexible piece of lead (46 g) secured to the paw (B1) by self‐adhesive, elastic tape (B2). Under these conditions, the knee extensor (VL) activity was disrupted, but burst durations of ankle flexor (TA) and extensor (LG) muscles and their reciprocal activity were not perturbed.

Adapted from Fig. of Smith and Zernicke
Figure 7. Figure 7.

Swing‐phase kinematics and kinetics of the human knee joint for walking (1.67 m · s−1) and running (4.16 m · s1). At the top of each panel, the position of the leg is shown at various stages of swing, from toe‐off to heel contact. Upper plots show the angular displacement (solid line) and velocity (dashed line) for the knee joint. Middle plots illustrate the NET torque at the knee, and its three main components: NET = gravity (GRA) + muscle (MUS) + summed motion‐dependent torque (MDT). Positive values represent flexor torques; negative values represent extensor torques. Data are normalized to the percentage of swing, and torque data are normalized to subject mass (Nm/kg).

Unpublished data from Zernicke et al.
Figure 8. Figure 8.

Angular displacements and EMG for three speeds (human). Displacement data are normalized to percentage of step cycle, 0% = heel strike (stance onset) and 100% = toe‐off (swing onset). Stance is indicated by a bar at the top of each record. GM, gluteus maximus (hip extensor); RF, rectus femoris (hip flexor, knee extensor; see text for explanation of arrows); VL, vastus lateralis (knee extensor); St‐Sm, semitendinosus–semimembranous (hip extensor, knee flexor); LG, lateral gastrocnemius (knee flexor, ankle extensor); TA, tibialis anterior (ankle flexor).

Adapted from Fig. of Nilsson et al.
Figure 9. Figure 9.

Two forms of walking for the cat. The cat's position at paw‐off (onset of swing) is illustrated for forward (FWD) walking, and the cat's position at paw contact (onset of stance) is shown for backward (BWD) walking.

Adapted from Fig. of Smith et al. .] Typical EMG records and angular displacement for the hip, knee, and ankle are also illustrated for both forms of walking. ABF, anterior biceps femoris (hip extensor); VL, vastus lateralis (knee extensor); LG, lateral gastrocnemius (knee flexor, ankle extensor); ST, (hip extensor, knee flexor); TA, ankle flexor. Arrows at the top mark paw‐off (up arrow) and paw contact (down arrow). [Adapted from Fig. of Perell et al.
Figure 10. Figure 10.

Average swing‐phase kinetics at a cat knee joint for several forward (FWD) and backward (BWD) steps at 0.6 m · s−1. Positive values represent extensor torques, and negative values represent flexor torques; the dashed horizontal line indicates zero torque. Dotted vertical lines indicate the reversal from flexion to extension (F–E1) at the knee joint. Torque components are: net torque (NET), gravitational torque (GRA), sum of the motion‐dependent (MDT), and the muscle (MUS).

Adapted from Fig. of Perell et al.
Figure 11. Figure 11.

Average swing‐phase kinetics for the cat knee joint for several trot and gallop steps at 2.25 m · s−1. Vertical line marks the F–E1 transition. Torque components are: net torque (NET), gravitational torque (GRA), sum of motion dependent (MDT), and the muscle (MUS); here, motion‐dependent torque components include leg angular acceleration (LAA) and hip linear acceleration (HLA). Positive values represent extensor torques, and negative values represent flexor torques. Time marks indicate 30 ms intervals.

Adapted from Fig. of Smith et al.
Figure 12. Figure 12.

Rectified‐averaged EMG records from the semitendinosus (ST) for two speeds of walking, trotting, and galloping of two cats (A and B). The time‐averaged records were triggered from the onset of the flexor‐related burst at paw‐off (STpo), marked by vertical lines. A total of 62 steps were averaged for cat A and 64 steps for cat B. Scale bars: horizontal, 80 ms; vertical, 1.0 mV for cat A and 0.5 mV for cat B.

Taken from Fig. of Smith et al. with publisher's permission
Figure 13. Figure 13.

Averaged‐rectified EMG data of four biarticular muscles for several forward (A) and backward (B) treadmill steps (cat). Muscles are: medial and anterior sartorius (SAm, SAa), rectus femoris (RF), and the semitendinosus (ST). EMG data were averaged at paw‐off (arrow). Asterisks (*) indicate paw contact. With calibration settings in B taken as 1, settings in A are 1.25 for SAm, 1.5 for SAa, 2.25 for RF, and 2.75 for ST.

Adapted from Fig. of Pratt et al.
Figure 14. Figure 14.

Kinematics and muscle torque data for the normalized step cycle of two walking forms. Figurines at the top depict both behaviors. Angular displacement plots are redrawn from Vilensky et al. . All data are normalized to percentage of step cycle, starting at the onset of stance with heel contact (HC) for forward walking and toe contact (TC) for backward walking. Swing onset is marked by a vertical line at toe‐off (TO) for forward walking and heel‐off (HO) for backward walking. Stance and swing onsets are also indicated for the contralateral (c) leg. Kinetic data, normalized to body mass (N · m/kg), are redrawn from Winter et al. . Positive torque values indicate extensor muscle torques (EXT); dotted lines represent the coefficient of variation for the torque data.

Figure 15. Figure 15.

Kinematics of the cat's hindlimb for up‐ and down‐slope walking; slope at a 33% grade. Drawings above the graphs illustrate the cat's posture at contact for the left hind paw. The two shadowed figures show the cat's posture at the same instance for level walking. Within the graphs, the dashed lines represent the standard deviation of the angular displacement data for the knee joint. Data are graphed from the onset of swing and normalized to percentage of cycle. Vertical lines indicate the onset of stance at paw contact.

Unpublished data from Smith et al. and Smith and Carlson‐Kuhta
Figure 16. Figure 16.

Stance‐phase kinetics for walking in human and cat. The human leg (A) and cat hindlimb (C; joints are labeled: H, hip; K, knee; A, ankle; MPT, metatarsophalangeal) are illustrated for stance, beginning with heel contact (HC) and ending with toe‐off (TO) in A and beginning with paw contact (PC) and ending with paw‐off (PC) in C. In B and D, vertical (V) and horizontal (H) ground reaction force components are illustrated. Negative components for H are braking and positive are propulsive forces.

Force data in B are expressed in percentage of body weight and redrawn from Inman , and force data in D are absolute values (Newton, N) for a 49 N cat and redrawn from Fowler et al.
Figure 17. Figure 17.

Muscle (MUS) torques for the hip, knee, and ankle joints for the cat hindlimb during stance of forward (A) and backward (B) treadmill walking. Mean (solid line) and standard deviations (dashed lines) are data from four steps of one cat. For all plots, extensor torques are positive, and flexor torques are negative values.

Adapted from Fig. of Perell et al.
Figure 18. Figure 18.

The average muscle torque at the ankle and standard deviation curves calculated from the stance phase of three step cycles from walking cats. Lateral gastrocnemius (LG) and medial gastrocnemius (MG) muscle torques were calculated from one of these step cycles. Plantaris (PLT) and soleus (SOL) moments were calculated from two steps cycles from another cat. With these conditions in mind, the data demonstrate how each ankle extensor muscle contributes to a muscle torque of this magnitude during stance.

Adapted from Fig. of Fowler et al.
Figure 19. Figure 19.

A planar, three‐segment model of the arm (A). The directional property of the effective inertial behavior of the upper limb's end‐point is represented as an ellipse (B). Force vectors required to accelerate the end‐point are shown as arrows, and the vector from the head of the arrow to the origin of the coordinate frame represents the corresponding acceleration. Changes in the effective end‐point inertia of the limb that are achieved by changing the limb configuration (while the end‐point remains stationary) are shown as ellipses C, D, and E.

Adapted from Fig. of Hogan et al.
Figure 20. Figure 20.

A frontal (left side) and lateral view (right side) of experimental set‐up and subject position. Numbers denote the following: (1) circular black‐metal plate connected by a stem to a wooden‐dowel handle that subjects grasped; (2) light beams (photoelectric cells plus infrared LEDs) attached to the Plexiglas sheet with black arrows indicating the targets' positions; (3) T‐shaped barrier that subjects circumnavigated; (4) suspended, clear Plexiglas sheet with center slit; (5) straight‐backed chair; (6) seat belts; and (7) markers attached at the glenohumeral, elbow, wrist, and third metacarpophalangeal joints, and the center of the circular metal plate. Subjects started and ended the movement with the circular plate held steady in the lower light beam. The upper light beam only had to be interrupted by the metal plate as subjects reversed their upward motion to begin the downward phase of the task.

Adapted from Fig. of Schneider and Zernicke
Figure 21. Figure 21.

Exemplar hand paths for the upward phase, with acceleration vectors (sagittal plane) for a before‐practice (A) and an after‐practice movement (B). The “before‐practice” trial was the slowest time, although subjects were attempting to go “as fast as possible.” The movement time for each of the trials was the same, as subjects—after practicing the task—repeated the movement at the less than maximal speed. The hand path is the continuous curved line, whereas at successive and equal points in time, the linear acceleration vectors (denoting magnitude and direction) are shown as straight lines originating from the hand path. To scale the dimensions of the acceleration vectors to the dimensions of the hand path, the magnitudes of the acceleration vectors were multiplied by 0.005.

Taken from Fig. of Schneider and Zernicke , with publisher's permission
Figure 22. Figure 22.

Shoulder‐joint torques for a before‐practice (A) and after‐practice (B) movement during the reversal in the upper target. Positive torques tend to cause shoulder extension, and negative torques tend to cause shoulder flexion (lifting the arm). There is a difference of more than twofold in the ordinates of A and B. The torque components illustrated are: NET, net joint torque; MUS, muscle torque; GRA, gravitational torque; UAA, inertial torque related to upper arm angular acceleration.

Taken from Fig. of Zernicke and Schneider , with publisher's permission
Figure 23. Figure 23.

Hand paths, dynamics, and EMG for arm movements in two directions for a control (A) and deafferentated (B) subject. See text for description of the template‐tracing task. Ensemble averages for joint angles (top), elbow joint torque components (middle), and EMG records (bottom) are illustrated for movements made along the 0‐degree template (left) and the 125‐degree template (right). Torque components include an interaction torque (Inter; same as the motion‐dependent torque of equation ), a generalized muscle torque (Mus; same as the generalized muscle torque of equation ), and a self‐torque [Self = (− I · α)]; see Sainburg et al. for a comparison of the self‐torque and the net joint torque in equation . Data for each record are averaged across five trials and aligned to the zero cross (abscissa) in elbow joint flexor acceleration. Shading highlights the interval of flexor acceleration, encompassing the hand‐path reversal.

Adapted from Figs. and of Sainburg et al.
Figure 24. Figure 24.

Shoulder joint torques for representative reaches at week 17 (A) and week 51 (B). Absolute times within a 14 s epoch are given; the two reaches occurred at 5.5 s (A) and 2–3 s (B). Positive torques tend to cause shoulder extension, and negative torques tend to produce shoulder flexion. The torque components are: NET, net joint torque; MUS, generalized muscle torque; GRA, gravitational torque; MDT, sum of all motion‐dependent torques. Torques are normalized to infant's body weight (N) at the different ages.

Adapted from Fig. of Zernicke and Schneider
Figure 25. Figure 25.

Hand trajectories of all analyzable trials at reach onset (top record of each panel), onset plus 1 week (middle record), onset plus 2 weeks, (bottom record) during which the “active infant” (Nathan) and the “quiet infant” (Justin) contacted the toy (black dot). Only the trajectory of the hand contacting the toy is illustrated. Your perspective is from a top view (as though you were directly above each infant, looking down on his head as he faced the toy directly in front of him). Trajectories were normalized to the space‐time coordinates of the toy contact and are plotted for the last 3 s prior to hand‐toy contact.

Adapted from Figs. and of Thelen et al.


Figure 1.

Nonintuitive relations between torque and kinematics. Data are from a subject pointing forward, moving the hand in the sagittal plane to a target at shoulder level. The joint motions required were shoulder flexion (upward angle trace) and elbow extension (downward angle trace). While these opposite motions occurred, agonists for this action were shoulder flexors (e.g., anterior deltoid) and elbow flexors (e.g., biceps brachii), with shoulder and elbow joint torques that both had increased flexor influences.

Adapted from Fig. of Soechting and Flanders


Figure 2.

Interpretive and free‐body diagrams of a model of an infant's upper extremity. The upper diagram shows the limb positioned in an inertial (x‐y‐z) coordinate system. A positive torque is defined (M). The upper extremity is modeled as three interconnected rigid segments (S1 hand, S2 forearm, and S3 upper arm) with frictionless joints (J1 wrist, J2 elbow, and J3 shoulder). At each instant in time during a reach, a moving local plane (P) is calculated so that the plane contains the x‐y‐z coordinates of each of the three joint centers (J1, J2, J3). The planar torques at the wrist, elbow, and shoulder are calculated with respect to the respective joint axes (Z1', Z2', Z3') that pass through each joint center and are perpendicular to the moving local plane (P). In the lower portion of the figure is a free‐body diagram of the upper extremity. Depicted are forces related to the hand, forearm, and upper arm segment weights (W1, W2, W3) acting at their respective center of mass, and the wrist, elbow, and shoulder joint reaction forces (F1, F2, F3) and torques (M1, M2, M3).

Adapted from Fig. of Zernicke and Schneider


Figure 3.

Anatomical drawing of the cat hindlimb with a schematic of a force platform beneath it. E‐shaped tendon transducers are shown on the lateral gastrocnemius (LG) and tibialis anterior (TA) tendons. FR is the resultant ground reaction force vector acting on the plantar surface of the paw. Each force platform contains two piezoelectric transducers (TR). Digit (θd), tarsal (θt), and shank (θS) segment angles are calculated from the right horizontal. Ma is the muscle torque acting about the ankle joint.

Redrawn from Fig. (a) of Fowler et al.


Figure 4.

Hindlimb coordination for the paw shake. The response is tested with the spinalized cat held vertically; tape is wrapped around the paw (A). Positions at the start of a cycle (A1, peak ankle extension) and mid‐cycle (A2, peak ankle flexion) are shown. Hindlimb segments (thigh, leg, paw) are outlined; each joint (hip, knee, ankle) is marked by a dot. In B, EMG records of four cycles are from an ankle extensor (LG) and flexor (TA); knee extensor (VL) and hip extensor‐knee flexor (BF). Kinematics for four steady‐state cycles are shown in C; 50 ms intervals mark the abscissa. An angle‐angle plot in D illustrates knee‐ankle coordination for steady‐state cycles. Each cycle begins at peak ankle extension (a) and proceeds in a counterclockwise direction. First the knee extends and ankle flexes. Peak knee extension (b) precedes peak ankle flexion. Next, the knee flexes and later the ankle extends (c). Dots on the curve mark time intervals of 5 ms. Bars indicate timing of EMG bursts for LG and BF (stippled), VL (shaded), and TA (unshaded).

Adapted from Figs. and of Smith and Zernicke


Figure 5.

Torque components during a typical paw‐shake cycle. The net, muscle, and motion‐dependent torques are shown for the ankle (top) and knee (bottom) joints. The gravitational torque was negligible at both joints and is not illustrated. At the ankle, the main motion‐related torques (leg angular acceleration and knee linear acceleration) counterbalance each other, and the muscle torque dominated the net torque. Positive values represent flexor torques. At the knee, paw angular acceleration (the main inertial torque) is counterbalanced by muscle torque, and net torque is negligible. Positive values represent extensor torques. Bars show the timing of EMG bursts for extensor and flexor muscles at the ankle and knee. Records are aligned by cycle time; vertical lines mark kinematic events.

Adapted from Figs. A and A of Hoy et al.


Figure 6.

Disruption of knee extensor activity during paw‐shake responses elicited under two conditions. The EMG record in A shows a paw‐shake response with knee and ankle joint immobilized by a plaster cast, while the record in B shows a response with a flexible piece of lead (46 g) secured to the paw (B1) by self‐adhesive, elastic tape (B2). Under these conditions, the knee extensor (VL) activity was disrupted, but burst durations of ankle flexor (TA) and extensor (LG) muscles and their reciprocal activity were not perturbed.

Adapted from Fig. of Smith and Zernicke


Figure 7.

Swing‐phase kinematics and kinetics of the human knee joint for walking (1.67 m · s−1) and running (4.16 m · s1). At the top of each panel, the position of the leg is shown at various stages of swing, from toe‐off to heel contact. Upper plots show the angular displacement (solid line) and velocity (dashed line) for the knee joint. Middle plots illustrate the NET torque at the knee, and its three main components: NET = gravity (GRA) + muscle (MUS) + summed motion‐dependent torque (MDT). Positive values represent flexor torques; negative values represent extensor torques. Data are normalized to the percentage of swing, and torque data are normalized to subject mass (Nm/kg).

Unpublished data from Zernicke et al.


Figure 8.

Angular displacements and EMG for three speeds (human). Displacement data are normalized to percentage of step cycle, 0% = heel strike (stance onset) and 100% = toe‐off (swing onset). Stance is indicated by a bar at the top of each record. GM, gluteus maximus (hip extensor); RF, rectus femoris (hip flexor, knee extensor; see text for explanation of arrows); VL, vastus lateralis (knee extensor); St‐Sm, semitendinosus–semimembranous (hip extensor, knee flexor); LG, lateral gastrocnemius (knee flexor, ankle extensor); TA, tibialis anterior (ankle flexor).

Adapted from Fig. of Nilsson et al.


Figure 9.

Two forms of walking for the cat. The cat's position at paw‐off (onset of swing) is illustrated for forward (FWD) walking, and the cat's position at paw contact (onset of stance) is shown for backward (BWD) walking.

Adapted from Fig. of Smith et al. .] Typical EMG records and angular displacement for the hip, knee, and ankle are also illustrated for both forms of walking. ABF, anterior biceps femoris (hip extensor); VL, vastus lateralis (knee extensor); LG, lateral gastrocnemius (knee flexor, ankle extensor); ST, (hip extensor, knee flexor); TA, ankle flexor. Arrows at the top mark paw‐off (up arrow) and paw contact (down arrow). [Adapted from Fig. of Perell et al.


Figure 10.

Average swing‐phase kinetics at a cat knee joint for several forward (FWD) and backward (BWD) steps at 0.6 m · s−1. Positive values represent extensor torques, and negative values represent flexor torques; the dashed horizontal line indicates zero torque. Dotted vertical lines indicate the reversal from flexion to extension (F–E1) at the knee joint. Torque components are: net torque (NET), gravitational torque (GRA), sum of the motion‐dependent (MDT), and the muscle (MUS).

Adapted from Fig. of Perell et al.


Figure 11.

Average swing‐phase kinetics for the cat knee joint for several trot and gallop steps at 2.25 m · s−1. Vertical line marks the F–E1 transition. Torque components are: net torque (NET), gravitational torque (GRA), sum of motion dependent (MDT), and the muscle (MUS); here, motion‐dependent torque components include leg angular acceleration (LAA) and hip linear acceleration (HLA). Positive values represent extensor torques, and negative values represent flexor torques. Time marks indicate 30 ms intervals.

Adapted from Fig. of Smith et al.


Figure 12.

Rectified‐averaged EMG records from the semitendinosus (ST) for two speeds of walking, trotting, and galloping of two cats (A and B). The time‐averaged records were triggered from the onset of the flexor‐related burst at paw‐off (STpo), marked by vertical lines. A total of 62 steps were averaged for cat A and 64 steps for cat B. Scale bars: horizontal, 80 ms; vertical, 1.0 mV for cat A and 0.5 mV for cat B.

Taken from Fig. of Smith et al. with publisher's permission


Figure 13.

Averaged‐rectified EMG data of four biarticular muscles for several forward (A) and backward (B) treadmill steps (cat). Muscles are: medial and anterior sartorius (SAm, SAa), rectus femoris (RF), and the semitendinosus (ST). EMG data were averaged at paw‐off (arrow). Asterisks (*) indicate paw contact. With calibration settings in B taken as 1, settings in A are 1.25 for SAm, 1.5 for SAa, 2.25 for RF, and 2.75 for ST.

Adapted from Fig. of Pratt et al.


Figure 14.

Kinematics and muscle torque data for the normalized step cycle of two walking forms. Figurines at the top depict both behaviors. Angular displacement plots are redrawn from Vilensky et al. . All data are normalized to percentage of step cycle, starting at the onset of stance with heel contact (HC) for forward walking and toe contact (TC) for backward walking. Swing onset is marked by a vertical line at toe‐off (TO) for forward walking and heel‐off (HO) for backward walking. Stance and swing onsets are also indicated for the contralateral (c) leg. Kinetic data, normalized to body mass (N · m/kg), are redrawn from Winter et al. . Positive torque values indicate extensor muscle torques (EXT); dotted lines represent the coefficient of variation for the torque data.



Figure 15.

Kinematics of the cat's hindlimb for up‐ and down‐slope walking; slope at a 33% grade. Drawings above the graphs illustrate the cat's posture at contact for the left hind paw. The two shadowed figures show the cat's posture at the same instance for level walking. Within the graphs, the dashed lines represent the standard deviation of the angular displacement data for the knee joint. Data are graphed from the onset of swing and normalized to percentage of cycle. Vertical lines indicate the onset of stance at paw contact.

Unpublished data from Smith et al. and Smith and Carlson‐Kuhta


Figure 16.

Stance‐phase kinetics for walking in human and cat. The human leg (A) and cat hindlimb (C; joints are labeled: H, hip; K, knee; A, ankle; MPT, metatarsophalangeal) are illustrated for stance, beginning with heel contact (HC) and ending with toe‐off (TO) in A and beginning with paw contact (PC) and ending with paw‐off (PC) in C. In B and D, vertical (V) and horizontal (H) ground reaction force components are illustrated. Negative components for H are braking and positive are propulsive forces.

Force data in B are expressed in percentage of body weight and redrawn from Inman , and force data in D are absolute values (Newton, N) for a 49 N cat and redrawn from Fowler et al.


Figure 17.

Muscle (MUS) torques for the hip, knee, and ankle joints for the cat hindlimb during stance of forward (A) and backward (B) treadmill walking. Mean (solid line) and standard deviations (dashed lines) are data from four steps of one cat. For all plots, extensor torques are positive, and flexor torques are negative values.

Adapted from Fig. of Perell et al.


Figure 18.

The average muscle torque at the ankle and standard deviation curves calculated from the stance phase of three step cycles from walking cats. Lateral gastrocnemius (LG) and medial gastrocnemius (MG) muscle torques were calculated from one of these step cycles. Plantaris (PLT) and soleus (SOL) moments were calculated from two steps cycles from another cat. With these conditions in mind, the data demonstrate how each ankle extensor muscle contributes to a muscle torque of this magnitude during stance.

Adapted from Fig. of Fowler et al.


Figure 19.

A planar, three‐segment model of the arm (A). The directional property of the effective inertial behavior of the upper limb's end‐point is represented as an ellipse (B). Force vectors required to accelerate the end‐point are shown as arrows, and the vector from the head of the arrow to the origin of the coordinate frame represents the corresponding acceleration. Changes in the effective end‐point inertia of the limb that are achieved by changing the limb configuration (while the end‐point remains stationary) are shown as ellipses C, D, and E.

Adapted from Fig. of Hogan et al.


Figure 20.

A frontal (left side) and lateral view (right side) of experimental set‐up and subject position. Numbers denote the following: (1) circular black‐metal plate connected by a stem to a wooden‐dowel handle that subjects grasped; (2) light beams (photoelectric cells plus infrared LEDs) attached to the Plexiglas sheet with black arrows indicating the targets' positions; (3) T‐shaped barrier that subjects circumnavigated; (4) suspended, clear Plexiglas sheet with center slit; (5) straight‐backed chair; (6) seat belts; and (7) markers attached at the glenohumeral, elbow, wrist, and third metacarpophalangeal joints, and the center of the circular metal plate. Subjects started and ended the movement with the circular plate held steady in the lower light beam. The upper light beam only had to be interrupted by the metal plate as subjects reversed their upward motion to begin the downward phase of the task.

Adapted from Fig. of Schneider and Zernicke


Figure 21.

Exemplar hand paths for the upward phase, with acceleration vectors (sagittal plane) for a before‐practice (A) and an after‐practice movement (B). The “before‐practice” trial was the slowest time, although subjects were attempting to go “as fast as possible.” The movement time for each of the trials was the same, as subjects—after practicing the task—repeated the movement at the less than maximal speed. The hand path is the continuous curved line, whereas at successive and equal points in time, the linear acceleration vectors (denoting magnitude and direction) are shown as straight lines originating from the hand path. To scale the dimensions of the acceleration vectors to the dimensions of the hand path, the magnitudes of the acceleration vectors were multiplied by 0.005.

Taken from Fig. of Schneider and Zernicke , with publisher's permission


Figure 22.

Shoulder‐joint torques for a before‐practice (A) and after‐practice (B) movement during the reversal in the upper target. Positive torques tend to cause shoulder extension, and negative torques tend to cause shoulder flexion (lifting the arm). There is a difference of more than twofold in the ordinates of A and B. The torque components illustrated are: NET, net joint torque; MUS, muscle torque; GRA, gravitational torque; UAA, inertial torque related to upper arm angular acceleration.

Taken from Fig. of Zernicke and Schneider , with publisher's permission


Figure 23.

Hand paths, dynamics, and EMG for arm movements in two directions for a control (A) and deafferentated (B) subject. See text for description of the template‐tracing task. Ensemble averages for joint angles (top), elbow joint torque components (middle), and EMG records (bottom) are illustrated for movements made along the 0‐degree template (left) and the 125‐degree template (right). Torque components include an interaction torque (Inter; same as the motion‐dependent torque of equation ), a generalized muscle torque (Mus; same as the generalized muscle torque of equation ), and a self‐torque [Self = (− I · α)]; see Sainburg et al. for a comparison of the self‐torque and the net joint torque in equation . Data for each record are averaged across five trials and aligned to the zero cross (abscissa) in elbow joint flexor acceleration. Shading highlights the interval of flexor acceleration, encompassing the hand‐path reversal.

Adapted from Figs. and of Sainburg et al.


Figure 24.

Shoulder joint torques for representative reaches at week 17 (A) and week 51 (B). Absolute times within a 14 s epoch are given; the two reaches occurred at 5.5 s (A) and 2–3 s (B). Positive torques tend to cause shoulder extension, and negative torques tend to produce shoulder flexion. The torque components are: NET, net joint torque; MUS, generalized muscle torque; GRA, gravitational torque; MDT, sum of all motion‐dependent torques. Torques are normalized to infant's body weight (N) at the different ages.

Adapted from Fig. of Zernicke and Schneider


Figure 25.

Hand trajectories of all analyzable trials at reach onset (top record of each panel), onset plus 1 week (middle record), onset plus 2 weeks, (bottom record) during which the “active infant” (Nathan) and the “quiet infant” (Justin) contacted the toy (black dot). Only the trajectory of the hand contacting the toy is illustrated. Your perspective is from a top view (as though you were directly above each infant, looking down on his head as he faced the toy directly in front of him). Trajectories were normalized to the space‐time coordinates of the toy contact and are plotted for the last 3 s prior to hand‐toy contact.

Adapted from Figs. and of Thelen et al.
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Ronald F. Zernicke, Judith L. Smith. Biomechanical Insights into Neural Control of Movement. Compr Physiol 2011, Supplement 29: Handbook of Physiology, Exercise: Regulation and Integration of Multiple Systems: 293-330. First published in print 1996. doi: 10.1002/cphy.cp120108