A study of the human gait cycle in order to design a biped robot

To make a biped walking machine, it seems to me essential to understand as we walk. This is precisely the aim of the study. It differs from other studies because the pelvis and chest (pectoral girdle and arm) are taken into account.

1      Take a closer look at human gait

1.1    Introduction

Biomechanics defines walking a form of bipedal locomotion as there is an alternating action between lower extremities. One leg is in touch with the ground for restraining, supporting and propulsion.

The other leg is in swing phase for creating a new step forward. So gait is the result of a series of rhythmic alternating movement of arms, legs, and trunk which create forward movement of the body.

By convention, the gait cycle begins with the initial placement off the right heel and ends when the same heel contacts the ground.

A cycle can be decomposed in phases as follows (see Figure 1 and [6]):

• Stance phase, itself divided into:
• Loading response. This phase begins with the heel strike, the folding of the foot on the ground and the period of initial double support (between 0 and 12% of the gait cycle). Its role is to transfer the weight of the body towards the supporting leg, maintain speed and balance the center of gravity of the body by absorbing energy through a "suppressive" action of the muscles of the leg;
• Mid-stance phase. This phase corresponds to the response of the ground on the foot and the first half of single support (12-34% of the cycle). It communicates the full charge of the body to the supporting leg and allows the body forward over the foot. This phase ends when the center of gravity of the body is located directly above the supporting foot. Its role is to anchor the foot to the floor so that it will become the pivot of the supporting leg;
•  Terminal Stance phase. This phase corresponds to the second half of the single-foot support (34 to 50% of the cycle). The body goes vertically from the center of pressure of the supporting leg and swing out to the contact of the opposite foot with the ground. Its role is to propel the body forward;
   
• Pre-swing phase. It corresponds to the second double support period (50-62% of the cycle). The body weight is transferred to the swing leg. Its role is to create an impulse on the forefoot on the ground in order to push the leg forward.
• Swing phase is decomposed in three stages:
• Initial swing. It corresponds to the first third of the swing phase (62 to 75% of the cycle). It begins with lift of the foot from the floor and ends when the swinging foot is opposite to the stance foot. One important issue addressed during this phase is foot clearance of the floor;
• Mid Swing. It corresponds to the second tier of the swing phase (75-90% duty cycle). It begins when the swinging foot is opposite the stance foot and ends when the swinging limb is tibia vertical (hip and knee flexion postures are equal);
• Terminal Swing. It corresponds to the third tier of the swing phase and ends with the next heel strike (90 to 100% duty cycle).

As one can see on Figure 1, each phase starts and ends with an instantaneous picture of the position of the body. For instance, the “Loading response” phase starts with Initial Contact (IC) and ends with Opposite Toe off (OT). In the detailed description of the phases, what we will do is to provide a picture for the start and the end of each phase.

 

Figure 1: positions of the legs during a gait cycle – reference is the right leg (dark leg).

2      Body parts included in the study

For each phase of the gait cycle, we will detail the movements made ​​by certain body parts, specifically:

• Upper body (arms and pelvic girdle);
• The pelvis;
• The hips;
•  Knees;
• The ankles and feet.

 

We will give an overview of the movements of the upper body, pelvis and feet before presenting the various phases of the gait cycle. We also give the definition of some terms that we will use extensively.

We'll start with the notion of reference planes. Biomechanics, movements are generally described in reference planes. The latter comprises three planes and three axes:

 

Figure 2 : présentation of the three reference planes.

2.1    Upper body

We will focus only on the shoulder girdle and arms [2].

In general, rotation of the shoulder girdle is the same amplitude as  the pelvic girdle, that is to say 5-6 °, but of opposite direction.

Referring to Figure 3 – right picture (walking), one can observe that in the frontal plane, a rotational movement of the shoulder girdle in the opposite direction of the pelvic rotation, that reaches its maximum immediately after the double support phase (DS Double Support). That is to say, the shoulder will sag on the side of the leg which becomes a supporting leg. We assume that it contributes to the preservation of the balance for preparing the next oscillation.

Referring to Figure 4, right picture (walking), one can observe in the horizontal plane, a rotation of the shoulder girdle, again opposite to the pelvic rotation. But here the shoulder girdle reached its maximum amplitude just before the double support phase, remains unchanged during the double support phase and finally initiates a rotation in the opposite direction at the end of the double support phase. The shoulder girdle return to neutral at the mid-stance phase.

 

Figure 3: Rotation of the pelvic and shoulder girdle in the frontal plane.

 

Figure 4: Rotation of the pelvic and the shoulder girdle in the horizontal plane.

The rotation of the arms play an important role in maintaining balance when walking [3] Swinging arms in an opposing direction with respect to the lower-limb reduces the angular momentum of the body, balancing the rotational motion produced during walking. Although such pendulum-like motion of arms is not essential for walking, recent studies point that arm swing improves the stability and energy efficiency in human locomotion.

Amplitude or frequency of arm movements is determined by the gait, as the walking speed increases, the amplitude of the arm swing increases accordingly.

There is also a dissymmetry in range of motion - the forward rotation is more important than that backward one - see Figure 5.

 

Figure 5: Arm movements.

2.2    Pelvic

We will focus on two rotations:

• In the frontal plane, also called obliquity [8];
• In the horizontal plane.

As it is shown on the Figure 6, as the heel of the leading limb contacts the ground, the pelvis is nearly neutral. During loading response, the hip of the trailing leg begins to drop, increasing the magnitude of pelvic obliquity. Immediately after toe-off, pelvic obliquity reaches its greatest amplitude. The motion of the pelvis is then reversed, with the swing-side hip regaining its neutral position during midstance, and then lowering slightly just before heel contact. The peak of the "primary" component of pelvic obliquity occurs just after toe-off, while smaller fluctuations ("secondary" components), occur near the end of the single-support phase.

In general for a pelvic rotation of 6 to 8° in the horizontal plane, one can notice a primary peak of  3-4° and a secondary peak of 1-2° in the frontal plane.

 

Figure 6: Pelvic obliquity during the difference phases of the walking gait – Sagittal plane on the top, frontal plane on the bottom.

In the horizontal plane, the movement of the pelvis is simple - see Figure 7. It will be noted that the pelvis returns to its neutral position in the middle of the stance phase.

 

Figure 7 : Pelvic rotation in the horizontal plane.

2.3    HIP & Knee

Here we introduce the definitions of flexion and extension. Reference is made to Figure 8.

Flexion is a movement in the sagittal plane, which decreases the angle at the moving joint. Extension is the opposite movement, which increases the angle at the joint.

As we will see in the description of the gait cycle, the knee is always in flexion but the hip will be either in flexion or extension.

 


Figure 8: Flexion and extension

2.4    Feet and ankles

Let us start with some useful definitions  (voir Figure 9):

In the frontal plane:

•  Foot supination or under-pronation occurs when feet roll outwards, placing weight on the outside of the foot;
•  Pronation occurs when feet roll inwards, placing weight on the inside of the foot;

In the sagittal plane, the ankle joint permits two movements:

• Plantar flexion (=flexion), in which the foot is pointed downwards
• Dorsiflexion (=extension), in which the foot is raised

Dorsiflexion is a more limited movement (normal range: 10-30°) than plantar flexion (normal range 20-50°).

 

Figure 9: foot movements.

Figure 10 describes the different movements of the reference foot during the gait cycle [4]. After foot-strike, the foot unlocks and pronates during the first half of the stance phase (when the foot is on the ground). The term ‘peak’ pronation refers to the maximum point of pronation that the foot reaches whilst it is on the ground and this typically occurs at around 40% of the stance phase. For toe off to occur, the foot needs to become a rigid lever and so it re-supinates in order be in a favourable position to push off. In other words, all of those joints that unlocked to allow the foot to move through pronation, need to reverse the motion and lock back up again (re-supinate).

 

 Figure 10: Description of the foot movement during the gait cycle

3      The walk cycle in details

3.1    Loading response

For a description of each phase, I will rely on an animation realized by Francis Jasmin [5] who also published a website dedicated to animation and specially gait cycle – it’s worth it to take a look.
On each drawing I noted the movements that will be detailed later in the section.

The phase:

• Starts with the Initial contact (see Figure 11) which is an instantaneous point in time that occurs when the foot of the leading lower limb touches the ground;
• Ends with the Opposite Toe off event (see Figure 12) which occurs when the big toe of the foot of the trailing leg leaves the ground.

 

 

Figure 11: Start of the Loading phase - Initial Contact

 

Figure 12: end of the Loading phase - Opposite toe-off

 

3.1.1     Upper body

In the Sagittal plane, the arms having reached their maximum forward (left arm) and backward (right arm) positions will start to move in the opposite direction at the end of the loading phase.

In the frontal plane, the pelvic and shoulder lines are opposed and there is a rotation of the shoulder girdle in the direction of the right side. At the end of the loading phase, the distance between the right shoulder and the right hip is at its lowest. This rotation participates to the weight transfer on the right side and to the control of the balance.

In the horizontal plane, the shoulder girdle executes a rotation in the opposite direction of the pelvic rotation and it reaches its maximum amplitude.

The amplitude of the rotation of the shoulder girdle is the same order of magnitude as that of the pelvic one.

3.1.2     Pelvic

In the frontal plane, the obliquity of the pelvic reaches its secondary peak at “Initial Contact” event. That is to say that the pelvic sinks to reduce the distance between the heel of the foot and the ground. The objective is to reduce the shock when the heel will be in contact with the floor. At the end of the phase pelvic obliquity goes back to neutral.

In the horizontal plane, the pelvic rotates on the right hip and it has reached its maximum amplitude, between 6° to 10° depending of the stride length. During the loading phase it remains on that position.

3.1.3     Hip

In the sagittal plane the hip is about 30° of flexion.Although at the end of the phase there may be the initiation of a teensy bit of extension.

3.1.4     Knee

In the Sagittal plane, at Initial contact the knee is in about 5° of flexion. This is ideal for absorbing the “shock” of the Loading Response. During the loading phase, it will continue to flex up to 15-20°.

3.1.5     Ankle and foot

Ankle is close to its neutral position. This help to initiate a “heel rocker”.  It also places the ground reaction force vector behind the ankle, creating a plantarflexion moment.

A plantarflexion – around 10 to 15° - occurs at “heel strike” then it reverses its motion and dorsiflexes so that at the end of the loading phase then ankle is in neutral position.

Regarding the foot, it is in the « taligrade phase » [5], meaning that the heel is the pivot for the rotation of the foot.

The foot is slightly supinated (2 to 3°) at “heel strike” and then pronates to enable adaption to the terrain.

3.2    Mid stance  

In this phase, the full charge of the body is transferred to the supporting leg and allows the body forward over the foot. This phase ends when the center of gravity of the body is located directly above the supporting foot. Its role is to anchor the foot to the floor so that it will become the pivot of the supporting legMid-stance is a period between opposite toe-off and heel-rise.

This phase:

• Starts with the Opposite Toe-off event – see Figure 12;
• Ends with the “Heel rise” event – see Figure 13.

 

Figure 13: end of the midstance phase – heel rise.

3.2.1     Upper body

In the Sagittal plane, the arms having reached their maximum forward (left arm) and backward (right arm) positions they move in the opposite direction to align at the end of the mid-stance phase.

In the frontal plane. At the end of the loading phase, the distance between the right shoulder and the right hip is at its lowest. During the mid-stance phase the shoulder line rotates in the opposite direction and goes back to neutral.

In the horizontal plane, the shoulder girdle executes a rotation in the opposite direction of the pelvic rotation and it goes back to neutral.

3.2.2     Pelvic

In the frontal plane, pelvic obliquity is in neutral position.

In the horizontal plane, the pelvic, which rotates on the right hip, reached its maximum amplitude during the loading phase. It initiates a movement in the opposite direction in order to reach a neutral position at the end of the mid-stance phase.

3.2.3     Hip

In the Sagittal plane, throughout mid-stance the hip extends towards neutral, achieving a a position of about 5° of flexion by the end of the phase.

3.2.4     Knee

Very early in Midstance flexion ceases and the knee begins extending, reaching a position of about 10 ° of flexion.

3.2.5     Ankle and foot

In the Sagittal plan, throughout midstance, the ankle steadily dorsiflexes to about 10° degrees. This is the « ankle rocker » which allows progression over the weightbearing limb.

In the Frontal plane, through midstance the foot resupinates to form a rigid lever for propulsion.

3.3    terminal stance

The body goes vertically from the center of pressure of the supporting leg and swing out to the contact of the opposite foot with the ground. Its role is to propel the body forward.

The phase:

• Starts with the Heel rise event – see Figure 13;
• Ends with the Opposite Toe-off event –see Figure 14.

 

Figure 14 : End of the terminal stance phase – Opposite Initial Contact

3.3.1     Upper body

In the Sagittal plane, the arms are reaching their maximum forward (right arm) and backward (left arm) positions.

In the frontal plane. The shoulder line starts to rotate in the direction of the left side.

In the horizontal plane, the shoulder girdle executes a rotation in the opposite direction of the pelvic rotation from neutral at the end of the midstance phase to its maximum amplitude at the end of the terminal stance phase.

 3.3.2     Pelvic

In the frontal plane, pelvic obliquity is in neutral position.

In the horizontal plane, the pelvic, which rotates on the right hip, it initiates a movement from neutral to its maximum amplitude at the end of the terminal stance phase.

3.3.3     Hip

In the Sagittal plane, hip continues its extension from neutral to an extension of 10°.

3.3.4     Knee

In the Sagittal plane the knee continues extending, reaching 5° of flexion, then the motion is reversed and the knee begins to flex (primarily because of heelrise/Plantarflexion) to about 12-15° of flexion.

3.3.5     Ankle and foot

In the Sagittal plane, the heel begins to rise but the ankle continues dorsiflexion, reaching a peak of about 12°. Then just before pre-swing the ankle begins plantarflexing, reaching about 10° by the ebd of the terminal stance phase.

In the Frontal plane, as the heel rise, the toes remain flat on the ground. Just prior to toe off the foot will start to pronate in readiness for foot clearance in swing.

3.4    pre-swing

The body weight is transferred to the swing leg. Its role is to create an impulse on the forefoot on the ground in order to push the leg forward.

The phase:

• Starts with the Opposite Initial contact event – See Figure 14;
• Ends with the Toe-off event – see Figure 15.

 

Figure 15: End of the pre-swing phase – toe off.

3.4.1     Upper body

In the Sagittal plane, the arms are reaching their maximum forward (right arm) and backward (left arm) positions, they start to reverse.

In the frontal plane. The shoulder line starts to rotate in the direction of the left side. The distance between the left shoulder and the left hip is at its lowest.

In the horizontal plane, the shoulder girdle executed a rotation in the opposite direction of the pelvic rotation during the midstance phase and reached its maximum amplitude at the end of the terminal stance phase. During the pre-swing phase the position remains unchanged.

3.4.2     Pelvic

In the frontal plane, pelvic obliquity reaches its “primary peak” (See Section 2.3).

In the horizontal plane, the pelvic, will now rotate on the left hip, remains in its position.

3.4.3     Hip

In the Sagittal plane, there is a reversal of direction so that flexion to nearly neutral occurs.

3.4.4     Knee

In the Sagittal plane, there is a rapid flexion to about 40° of flexion.

3.4.5     Ankle and foot

In the Sagittal plane, the ankle initiates a rapid plantarflexion from 10° of dorsiflexion to 20° of plantarflexion.

In the Frontal plane, prior to toe off the foot will start to pronate in readiness for foot clearance in swing.

3.5    initial swing

This pahse begins with lift of the foot from the floor and ends when the swinging foot is opposite to the stance foot. One important issue addressed during this phase is foot clearance of the floor.

The phase:

• Starts with the Toe off event – see Figure 15.
• Ends with the Feet adjacent event – see Figure 16.

 

Figure 16: End of the initial swing phase – Feet adjacent.

3.5.1     Upper body

In the Sagittal plane, the arms which reached their maximum forward (right arm) and backward (left arm) positions, initiate a rotation towards neutral position.

In the frontal plane. The shoulder initiates a rotation in the opposite direction towards a neutral position.

In the horizontal plane, the shoulder girdle executed a rotation in the opposite direction of the pelvic The rotation will reach a neutral position at the end of the initial swing phase.

 

3.5.2     Pelvic

In the frontal plane, pelvic obliquity go back to neutral.

In the horizontal plane, the pelvic, which rotates on the left hip, initiates a movement towards neutral position.

3.5.3     Hip

In the Sagittal plane, as soon as the foot leaves the ground there is a rapid flexion to about 25 -30°.

3.5.4     Knee

In the Sagittal plane, during this phase the knee continues flexing reaching a peak about 60°. Then the motion is reversed and the knee begins extending, so that at the end of the phase, a position of 55° of flexion has been reached.

3.5.5     Ankle and foot

In the Sagittal plane, the ankle begins dorsiflexing in order to clear the toes during the swing, to about 10° of plantarflexion.

3.6    mid-swing

Mid-swing begins when the swinging foot is opposite the stance foot and ends when the swinging limb is tibia vertical (hip and knee flexion postures are equal).

The phase:

• Starts with the Feet Adjacent event – See Figure 16;
• Ends with Tibia Vertical event – See Figure 17.

 

Figure 17: End of the Mid-swing phase – Tibia vertical

3.6.1     Upper body

In the Sagittal plane, the arms rotates, the right arm is moving backward and the left arm is moving forward.

In the frontal plane. The shoulder initiates a rotation from neutral position to the right side.

In the horizontal plane, the shoulder girdle executed a rotation in the opposite direction of the pelvic. The rotation will reach is maximum amplitude at the end of the mid-swing phase.

3.6.2     Pelvic

In the frontal plane, pelvic obliquity starts to move towards its secondary peak.

In the horizontal plane, the pelvic, which rotates on the left hip, initiates a movement from neutral to its maximum amplitude that will be reached at the end of the mid-swing phase.

3.6.3     Hip

In the Sagittal plane, flexion slows then stop at the end of the phase at a position about 30°.

3.6.4     Knee

In the Sagittal plane, there is a rapid extension to a position about 20° of flexion.

3.6.5     Ankle and foot

In the Sagittal plane, dorsiflexion is completed as the ankle reaches neutral.

Nothing to say about the foot in this phase.

3.7    terminal swing

This phase:

Starts with the Tibia vertical event – See Figure 17

Ends with the Initial contact event - See Figure 11

3.7.1     Upper body

In the Sagittal plane, the arms having reached their maximum forward (left arm) and backward (right arm) positions.

In the frontal plane. The shoulder initiates a rotation from neutral position to the right side.

In the horizontal plane, the shoulder girdle executed a rotation in the opposite direction of the pelvic. The rotation will reach is maximum amplitude at the end of the mid-swing phase.

3.7.2     Pelvic

In the frontal plane, pelvic obliquity starts to move towards its secondary peak.

In the horizontal plane, the pelvic reached its maximum amplitude and remains in this position.

3.7.3     Hip

In the Sagittal plane, the hip at first holds steady and thenextends slightly to a position of about 30°.

3.7.4     Knee

In the Sagittal plane, during most of this phase the knee continues extending reaching or almost the neutral. Then the motion is reverses and the knee begins to flex so that at the end of the terminal swing phase a position of about 5 degrees of flexion has been achieved.

3.7.5     Ankle and foot

In the Sagittal plane, the ankle remains neutral.

Nothing to say about the foot in this phase.

 

Reference:

[1] Cailleux Marie-Noëlle (1994) « Amputation de la cuisse chez l’adulte actif : playdoyer our le CAT-CAM », Thèse de Docteur en Médecine, Université de Franche-Conté, Besancon.

[2] Ceccato Jean Charles, Mathieu de Sèze, Christine Azevedo and Jean-René Cazalets (2009) “Comparaison of trunk activity during gait initiation and walking in humans”, PLoS One: http://www.ncbi.nlm.nih.gov/pmc/articles/PMC2782139/

[3] Collins Steven H., Adamcyk Peter G. and Kuo Arthur D. (2009), “Dynamic arm swinging in human walking”, Proceedings of the royal society – Biological Sciences.

[4] Dawber D., Bristow I. and Mooney J. (1996) “The foot: problems in podiatry and dermatology”, London Martin Dunitz Medical Pocket Books.

[5] Lepoutre Jean-Philippe (2007) « Modélisation biomécanique du mouvement : vers un outil d’évaluation pour l’instrumentation en orthopédie », Thèse de Doctorat,  Université du Sud Toulon.

[6] Levine David, Richards Jim, Wittle Michael (2014) “Whittle’s Gait Analysis”, Published by Churchill Livingstone.

[7] Jasmin Francis qui offre un excellent tutorial sur la marche:

 http://www.fjasmin.net/walk_cycle_tutorial/index.html

[8] Michaud Stephanie B., Gard Stephen, Childress Dudly (2000), « A preliminary investigation of pelvic obliquity patterns during gait in persons with transtibial and transfemoral amputation », Journal of Rehabilitation Research and Development, Vol 37, No 1

[9] Plas F., Viel E., Blanc Y. (1979), “La marche humaine, Kinesiology dynamique, Biomécanique et Pathomécanique”, Paris Masson 2^ième Edition.

[10] Williams Richard (2012) « The Animator’s Survival Kit: A Manual of Methods, Principles and Formulas for Classical, Computer, Games, Stop motion and internet animators”, Faber and Faber Inc.