When gait cycle events have been defined, derived kinematic quantities are calculated and written to file.

Note that throughout this section, axes are described as follows:

Transverse axes are those axes which pass from one side of the body to the other;
Sagittal axes pass from the back of the body to the front; and
Frontal axes pass in a direction from the center of the body through the top of the head.

List of kinematic variables calculated by Plug-in Gait

The following table lists all the kinematic variables calculated by Plug-in Gait. It includes information describing each variable in terms of ordered rotations or goniometric definitions.

For example, knee rotation is a relative angle measured between the thigh as the proximal segment and the shank as the distal segment. Its 'goniometric' axis is fixed to the shank as the distal segment. Incidentally, this angle, although always calculated, is often omitted from reports because it is so difficult to measure with precision.

Foot rotation and foot progression, also known as foot alignment, are not expressed in terms of goniometric axes, since the ankle angles are not calculated as strict Cardan angles. Both rotations measure the alignment of the foot. The first is relative to the shank, and the second is measured as an absolute angle in the laboratory's transverse plane.

Absolute angles are measured relative to laboratory axes with the sagittal and transverse axes automatically selected according to the direction of walking. In Plug-in Gait, the laboratory axis closest to the subject's direction of progression is labeled the laboratory sagittal axis.

Each variable is listed in the following table.

Angle rotation	Goniometric	Description
Pelvic tilt	Absolute	Pelvic tilt is normally calculated about the laboratory's transverse axis. If the subject's direction of forward progression is closer to the laboratory's sagittal axis, however, then pelvic tilt is measured about this axis. The sagittal pelvic axis, which lies in the pelvis transverse plane, is normally projected into the laboratory sagittal plane. Pelvic tilt is measured as the angle in this plane between the projected sagittal pelvic axis and the sagittal laboratory axis. A positive value (up) corresponds to the normal situation in which the PSIS is higher than the ASIS.
Pelvic obliquity	Absolute	Pelvic obliquity is measured about an axis of rotation that is perpendicular to the axes of the other two rotations. This axis does not necessarily correspond with any of the laboratory or pelvic axes. Pelvic obliquity is measured in the plane of the laboratory transverse axis and the pelvic frontal axis. The angle is measured between the projection into the plane of the transverse pelvic axis and projection into the plane of the laboratory transverse axis (the horizontal axis perpendicular to the subject's axis of progression). A positive pelvic obliquity value (up) relates to the situation in which the same side of the pelvis is higher.
Pelvic rotation	Absolute	Pelvic rotation is calculated about the frontal axis of the pelvic co-ordinate system. It is the angle measured between the sagittal axis of the pelvis and the sagittal laboratory axis (axis closest to subject's direction of progression) projected into the pelvis transverse plane. A negative (external) pelvic rotation value means the opposite side is in front.
Hip flexion/extension	Relative	Hip flexion is calculated about an axis parallel to the pelvic transverse axis which passes through the hip joint center. The sagittal thigh axis is projected onto the plane perpendicular to the hip flexion axis. Hip flexion is then the angle between the projected sagittal thigh axis and the sagittal pelvic axis. A positive (Flexion) angle value corresponds to the situation in which the knee is in front of the body.
Hip ab/adduction	Relative	Hip adduction is measured in the plane of the hip flexion axis and the knee joint center. The angle is calculated between the long axis of the thigh and the frontal axis of the pelvis projected into this plane. A positive number corresponds to an adducted (inwardly moved) leg.
Hip rotation	Relative	Hip rotation is measured about the long axis of the thigh segment and is calculated between the sagittal axis of the thigh and the sagittal axis of the pelvis projected into the plane perpendicular to the long axis of the thigh. The sign is such that a positive hip rotation corresponds to an internally rotated thigh.
Knee flexion/extension	Relative	The sagittal shank axis is projected into the plane perpendicular to the knee flexion axis. Knee flexion is the angle in that plane between this projection and the sagittal thigh axis. The sign is such that a positive angle corresponds to a flexed knee.
Knee ab/adduction (Knee varus/valgus)	Relative	This is measured in the plane of the knee flexion axis and the ankle center, and is the angle between the long axis of the shank and the long axis of the thigh projected into this plane. A positive number corresponds to varus (outward bend of the knee).
Knee rotation	Relative	Knee rotation is measured about the long axis of the shank. It is measured as the angle between the sagittal axis of the shank and the sagittal axis of the thigh, projected into a plane perpendicular to the long axis of the shank. The sign is such that a positive angle corresponds to internal rotation. If a tibial torsion value is present in the Session form, it is subtracted from the calculated knee rotation value. A positive tibial torsion value therefore has the effect of providing a constant external offset to knee rotation.
Ankle dorsi/plantar flexion	Relative	The foot vector is projected into the foot sagittal plane. The angle between the foot vector and the sagittal axis of the shank is the foot dorsi/plantar flexion. A positive number corresponds to dorsiflexion.
Foot rotation	Relative	This is measured about an axis perpendicular to the foot vector and the ankle flexion axis. It is the angle between the foot vector and the sagittal axis of the shank, projected into the foot transverse plane. A positive number corresponds to an internal rotation.
Foot-based dorsi/plantar flexion		This optional angle is defined similarly to ankle dorsi/plantar flexion, but it is measured in a plane containing the knee and ankle centers and the toe marker.
Foot progression	Absolute	This is the angle between the foot vector (projected into the laboratory's transverse plane) and the sagittal laboratory axis. A positive number corresponds to an internally rotated foot.
Head tilt	Absolute	Head tilt is normally calculated about the laboratory's transverse axis. If the subject's direction of forward progression is closer to the laboratory's sagittal axis, however, then head tilt is measured about this axis. The sagittal head axis is normally projected into the laboratory sagittal plane. Head tilt is measured as the angle in this plane between the projected sagittal head axis and the sagittal laboratory axis. A positive value (up) corresponds to backward head tilt.
Head obliquity	Absolute	Head lateral tilt is measured about an axis of rotation perpendicular to the axes of the other two rotations. This axis does not necessarily correspond with any of the laboratory or head axes. Head lateral tilt is measured in the plane of the laboratory transverse axis and the head frontal axis. The angle is measured between the projection into the plane of the transverse head axis and projection into the plane of the laboratory transverse axis (the horizontal axis perpendicular to the subject's axis of progression). A positive head obliquity value (up) relates to the situation in which the same side of the head is higher.
Head rotation	Absolute	Head rotation is calculated about the frontal axis of the head co-ordinate system. It is the angle measured between the sagittal axis of the head and the sagittal laboratory axis (axis closest to subject's direction of progression) projected into the head transverse plane. A negative (external) head rotation value means the opposite side is in front.
Thorax tilt	Absolute	Thorax tilt is normally calculated about the laboratory's transverse axis. If the subject's direction of forward progression is closer to the laboratory's sagittal axis, however, then thorax tilt is measured about this axis. The sagittal thorax axis is normally projected into the laboratory sagittal plane. Thorax tilt is measured as the angle in this plane between the projected sagittal thorax axis and the sagittal laboratory axis. A positive value (up) corresponds to forward thorax tilt.
Thorax obliquity	Absolute	Thorax obliquity is measured about an axis of rotation perpendicular to the axes of the other two rotations. This axis does not necessarily correspond with any of the laboratory or thorax axes. Thorax obliquity is measured in the plane of the laboratory transverse axis and the Thorax frontal axis. The angle is measured between the projection into the plane of the transverse thorax axis and projection into the plane of the laboratory transverse axis (the horizontal axis perpendicular to the subject's axis of progression. As the thorax segment is defined with the frontal Z axis point downward a positive (up) thorax obliquity angle relates to the situation in which the opposite side of the thorax is lower.
Thorax rotation	Absolute	Thorax rotation is calculated about the frontal axis of the thorax co-ordinate system. It is the angle measured between the sagittal axis of the thorax and the sagittal laboratory axis (axis closest to subject's direction of progression) projected into the thorax transverse plane. As the thorax segment is defined with the frontal Z axis point downward a positive (internal) thorax rotation value means the opposite side is behind .
Neck flexion/extension	Relative	The sagittal head axis is projected onto the plane perpendicular to the thorax sagittal axis. Neck flexion is then the angle between the projected sagittal head axis and the sagittal thorax axis around the fixed transverse axis of the thorax. A positive (flexion) angle value corresponds to the situation in which the head is tilted forward.
Neck lateral flexion	Relative	The angle between the long axis of the head and the long axis of the thorax around a floating transverse axis.
Neck rotation	Relative	Neck rotation is measured about the long axis of the head. It is measured as the angle between the sagittal axis of the head and the sagittal axis of the thorax, around a floating frontal axis. As the thorax frontal axis points downward while the head frontal axis points upward, a positive angle therefore refers to rotation of the head toward the opposite side.
Spine flexion/extension	Relative	Spine flexion is the angle between the sagittal thorax axis and the sagittal pelvis axis around the fixed transverse axis of the pelvis. A positive (flexion) angle value corresponds to the situation in which the thorax is tilted forward.
Spine lateral flexion	Relative	The angle between the long axis of the thorax and the long axis of the pelvis, around a floating transverse axis.
Spine rotation	Relative	It is measured as the angle between the sagittal axis of the thorax and the sagittal axis of the pelvis, around a floating frontal axis. As the thorax frontal axis points downward while the pelvis frontal axis points upward, a positive angle therefore refers to rotation of the thorax toward the opposite side.
Shoulder flexion/extension	Relative	Shoulder flexion is calculated about an axis parallel to the thorax transverse axis. Shoulder flexion is the angle between the projected sagittal-humerus axis and the sagittal-thorax axis around the fixed transverse axis. of the thorax. A positive (flexion) angle value corresponds to the situation in which the arm is in front of the body.
Shoulder ab/adduction	Relative	The angle is calculated between the transverse axis of the humerus and the transverse axis of the thorax around a floating sagittal axis. A negative number corresponds to an abducted (outwardly moved) arm.
Shoulder rotation	Relative	Shoulder rotation is measured about the long axis of the humerus segment and is calculated between the sagittal axis of the humerus and the sagittal axis of the thorax around a floating frontal axis. The sign is such that a positive shoulder rotation corresponds to an internally rotated humerus.
Elbow flexion/extension	Relative	Elbow flexion is the only kinematic parameter calculated at the elbow as the segment definitions of the Humerus and radius result in two of the axes being shared. Elbow flexion is calculated between the sagittal radius axis and the sagittal humerus axis around the fixed transverse axis of the humerus. A positive number indicates a flexion angle.
Wrist flexion/extension	Relative	Wrist flexion is the angle between the sagittal hand axis and the sagittal radius axis around the fixed transverse axis of the radius. A positive (flexion) angle value corresponds to the situation in which the wrist bends toward the palm.
Wrist ab/adduction	Relative	The angle is calculated between the transverse axis of the hand and the transverse axis of the radius around a floating sagittal axis. A positive number corresponds to the hand abducting toward the thumb.
Wrist rotation	Relative	Wrist rotation is measured about the long axis of the hand segment and is calculated between the sagittal axis of the hand and the sagittal axis of the radius around a floating frontal axis. The sign is such that a positive wrist rotation corresponds to the hand rotating in the direction of the thumb.

Complete pelvis position description

A pelvis in which the three markers all lay in the horizontal plane and the line joining the ASIS markers was parallel to a laboratory axis, would have zero tilt, obliquity and rotation.

To visualize the pelvic angles, start with a pelvis in this neutral position, tilt it about the transverse axis by the amount of pelvic tilt, rotate it about its (tilted) sagittal axis by the amount of pelvic obliquity and rotate it about its (tilted and oblique) frontal axis by the amount of pelvic rotation. The pelvis is now in the attitude described by those degrees of tilt, obliquity and rotation.

The transverse and frontal plane kinematics of all joints are influenced by the mathematics involved with embedded axes. The following is an example which demonstrates the effect of using embedded axes to calculate "pelvic obliquity" in a static trial: If a calibration device, designed with 15 degrees of pelvic tilt and level ASIS markers, is statically rotated 20 degrees from a lab's axis of progression, a report generated by Plug-in Gait will show 10 degrees of pelvic obliquity. For more clarification about the effect of embedded axes on joint kinematics, refer to Kadaba, Ramakrishnan and Wooten (1990).

Complete hip position description

A thigh whose long axis was parallel to the frontal pelvic axis, and in which the knee flexion axis was parallel to the pelvic transverse axis, would be in the neutral position (described by zeroes in all three angles). To move from this neutral position to the actual thigh position described by the three angles, first flex the hip by the amount of the hip flexion, then adduct by the amount of hip adduction, then rotate the thigh about the (flexed and adducted) long axis of the thigh, and it is in the position described by those three angles.

Complete knee position description

A neutral shank is positioned such that the shank is in line with the thigh and the ankle flexion axis is parallel to the knee flexion axis. From this position, flex the knee by the amount of knee flexion, bend inward by the amount of valgus/varus, and rotate by the amount of knee rotation, to produce the actual position described by those three angles.

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