3.2 Kinematics and Kinetics of Human Movement

Kinematics and kinetics are the two pillars of human movement analysis. Kinematics describes how the body moves, while kinetics explains why it moves. Together, they let you break down any activity, from a simple step to a baseball pitch, into measurable quantities.

Both fields apply Newton's laws to the human body. By studying linear and angular motion, joint torques, and muscle forces, engineers can quantify what's happening during movement. That information feeds directly into clinical gait analysis, injury prevention, prosthetic design, and rehabilitation planning.

Kinematics and kinetics of human movement

Principles of kinematics and kinetics

Kinematics studies motion without considering the forces that cause it. It focuses on position, velocity, and acceleration of body segments as they move through space.

Kinetics studies the forces behind that motion. These include:

• External forces like gravity, ground reaction forces, and air resistance
• Internal forces generated by muscles and transmitted through tendons, joints, and bones

Human movement involves the coordinated action of multiple body segments, each with its own linear and angular motion characteristics. Kinematics and kinetics give you the tools to analyze activities like walking, running, jumping, and throwing in precise, quantitative terms.

Applications of kinematics and kinetics in human movement analysis

• Gait analysis is one of the most common applications. Clinicians track the linear and angular motion of body segments during walking or running to assess both normal and pathological movement patterns (e.g., comparing a patient's gait after ACL reconstruction to a healthy baseline).
• Applying Newton's laws lets you quantify the forces involved in movement, which helps identify injury mechanisms and guide treatment design.
• Analyzing joint torques and muscle forces reveals the biomechanical demands of specific activities and how those demands change with pathology, aging, or training.

Linear and angular motion of the body

Linear motion of body segments

Linear motion is movement along a straight line (or, more precisely, translation where every point on the segment moves the same distance in the same direction). It's characterized by three variables:

• Position (where the segment is)
• Velocity (how fast and in what direction it's moving, $v = \frac{\Delta x}{\Delta t}$)
• Acceleration (how its velocity is changing, $a = \frac{\Delta v}{\Delta t}$)

In practice, body segments rarely move in pure straight lines. Most human movements combine linear and angular motion. Researchers capture this using tools like optical motion capture systems and high-speed video analysis.

Angular motion of body segments

Angular motion is the rotation of a body segment about an axis, such as the elbow joint acting as a pivot during a bicep curl. It's characterized by:

• Angular position ($\theta$, measured in degrees or radians)
• Angular velocity ($\omega = \frac{\Delta \theta}{\Delta t}$)
• Angular acceleration ($\alpha = \frac{\Delta \omega}{\Delta t}$)

Angular motion is central to most human activities. Swinging your arms during walking, rotating your trunk during a throw, and flexing your knee during running are all rotational. Analyzing angular motion reveals joint range of motion, movement efficiency, and potential injury risks. For example, excessive angular velocity at the shoulder during a baseball pitch can signal increased risk of rotator cuff injury.

Newton's laws of motion in human movement

Newton's first law (law of inertia)

An object at rest stays at rest, and an object in motion stays in motion at constant velocity, unless acted upon by an unbalanced force.

For human movement, this means your body won't start, stop, or change direction without a net force. A person standing still remains standing until a force (like a muscle contraction pushing against the ground) initiates movement. Inertia also explains why heavier limbs or body segments require greater force to accelerate or decelerate.

Newton's second law (law of acceleration)

The acceleration of an object is directly proportional to the net force acting on it and inversely proportional to its mass:

$F = ma$

This is the most frequently used law in biomechanical analysis. A stronger muscle contraction generates a greater net force on a body segment, producing a larger acceleration. Conversely, a more massive limb accelerates less for the same applied force. The angular equivalent is $\tau = I\alpha$, where $\tau$ is torque, $I$ is the moment of inertia, and $\alpha$ is angular acceleration.

Newton's third law (law of action-reaction)

For every action, there is an equal and opposite reaction.

When you jump, your feet push down on the ground, and the ground pushes back up on you with an equal force. That upward push is the ground reaction force (GRF), and it's what actually propels you into the air. Force plates embedded in laboratory floors measure GRFs directly, making this law the foundation of kinetic gait analysis.

Application of Newton's laws in human movement analysis

To analyze the dynamics of any movement, you account for all forces acting on each body segment:

1. Identify the external forces (gravity, GRFs, air resistance, contact forces from equipment).
2. Identify the internal forces (muscle contractions, joint reaction forces, ligament tensions).
3. Sum these forces to find the net force on each segment.
4. Use $F = ma$ (or $\tau = I\alpha$ for rotation) to relate that net force to the segment's acceleration.

This process lets you work forward (predicting motion from known forces) or backward (calculating forces from observed motion). The backward approach is called inverse dynamics and is covered in the next section.

Joint torques and muscle forces

Joint torques

A joint torque (or joint moment) is the rotational effect of forces acting about a joint. Torque depends on both the magnitude of the force and its moment arm, which is the perpendicular distance from the line of force to the joint center:

$\tau = F \times d$

where $F$ is the force and $d$ is the moment arm.

During walking, the hip, knee, and ankle each produce torques that must be precisely coordinated for a stable, efficient gait. If one joint's torque is too large or poorly timed, the whole pattern breaks down, which is exactly what clinicians look for in pathological gait.

Muscle forces

Muscles generate linear forces through the contraction of muscle fibers. These forces are transmitted through tendons to bones, creating the torques described above.

A few key points about muscle forces:

• The torque a muscle produces at a joint depends not just on how hard it contracts, but on its moment arm relative to the joint. A muscle with a small moment arm must generate a much larger force to produce the same torque.
• Most movements involve multiple muscles working together. In a bicep curl, the biceps brachii is the primary mover, but the brachialis and brachioradialis also contribute to elbow flexion. Antagonist muscles (like the triceps) co-contract to stabilize the joint.
• Muscle force magnitude changes with joint angle, contraction speed, and fiber length, which is why biomechanical models must account for these variables.

Inverse dynamics

Inverse dynamics is the standard technique for calculating joint torques and muscle forces from observed motion. Instead of predicting how a body will move given known forces (forward dynamics), you work backward from measured motion to figure out what forces must have caused it.

The process works like this:

1. Measure body segment positions over time using motion capture.
2. Differentiate position data to get velocities and accelerations.
3. Measure external forces (typically GRFs from a force plate).
4. Model the body as a chain of rigid linked segments, each with known mass and inertia properties.
5. Apply Newton's second law ($F = ma$ and $\tau = I\alpha$) to each segment, starting from the most distal segment (e.g., the foot) and working up the chain.
6. Solve for the unknown joint reaction forces and net joint torques at each joint.

Inverse dynamics is widely used in clinical gait labs, sports biomechanics, and ergonomic assessments. It provides quantitative data on how hard each joint is working during an activity, which is valuable for comparing pre- and post-surgical function, evaluating athletic technique, and understanding how aging or disease alters movement demands.