Kinematics vs Dynamics

What Is It?

Kinematics and dynamics are two distinct but related branches of mechanics. Kinematics describes the geometry of motion — the position, velocity and acceleration of bodies — without considering the forces that cause that motion. Dynamics extends kinematics by adding forces: it determines what forces and moments produce a given motion, or what motion results from given forces and moments. For structural load extraction from mechanisms, the distinction is critical. A kinematic analysis alone can tell you where every body is and how fast it is moving, but it cannot tell you the loads on the joints, bearings or supports. Only a dynamic analysis produces the reaction forces and moments that the surrounding structure must carry.

Why It Matters

A common and dangerous error is to assume that knowing the position of a mechanism — where each link is, what angle each joint has reached — is sufficient to determine the loads. It is not. Position tells you geometry. Load depends on how the mechanism is moving and how fast it is accelerating. Two identical mechanisms in the same position but with different velocities and accelerations will have completely different joint reactions. An actuator holding a control surface at 20 degrees in a static condition produces one set of loads; the same surface passing through 20 degrees during a rapid deployment produces quite different loads because of inertial effects. Position alone does not determine load.

KNOWING THE POSITION OF A MECHANISM DOES NOT TELL YOU THE LOAD WITHOUT KNOWING HOW IT IS MOVING.

Kinematics — The Geometry of Motion

Kinematics describes motion in terms of position, velocity and acceleration. Position is where a body is at a given instant. Velocity is the rate of change of position — how fast and in what direction the body is moving. Acceleration is the rate of change of velocity — how quickly the velocity is changing. For rotational motion, the equivalents are angular position (orientation), angular velocity and angular acceleration. These quantities are purely geometric — they describe what is happening without asking why. A kinematic analysis can be performed entirely from geometry and prescribed motion without any knowledge of mass, force or inertia.

Velocity:
  v  =  dx/dt          [m/s]

Acceleration:
  a  =  dv/dt  =  d²x/dt²          [m/s²]

Angular velocity:
  ω  =  dθ/dt          [rad/s]

Angular acceleration:
  α  =  dω/dt          [rad/s²]

Dynamics — Adding Forces

Dynamics adds the forces and moments that produce or result from motion. Newton's second law, F = ma, is the simplest statement: the net force on a body equals its mass times its acceleration. For real mechanisms, however, this is only the starting point. A mechanism contains joints that constrain motion, and those constraints generate reaction forces. A rotating body has angular acceleration, which requires a net moment. The full dynamic problem involves not just the applied forces but also the constraint reactions and the rotational equations of motion. The constraint reactions are precisely the interface loads that must be extracted for structural assessment.

Translational (Newton's second law):
  F  =  m · a          [N]

Rotational (simple principal-axis case):
  M  =  I · α          [N·m]

where:
F  =  net force
m  =  mass
a  =  acceleration
M  =  net moment
I  =  mass moment of inertia about the rotation axis
α  =  angular acceleration

Kinematics vs Dynamics — The Full Comparison

The table below contrasts kinematics and dynamics across the dimensions that matter for structural load extraction. The key insight is that kinematics can be performed in isolation — it produces motion — but dynamics is required to produce the loads that the structural model needs.

The Chain from Position to Reaction

The relationship between kinematics and dynamics can be visualised as a chain. Position evolves into velocity, which evolves into acceleration. Acceleration, combined with mass, produces inertial force. Inertial force, combined with applied forces and constraint reactions, produces the equilibrium that determines the joint reactions. Each step depends on the previous one. Skipping from position directly to load — as a static position analysis does — breaks the chain and loses the inertial contribution that often dominates in rapidly moving mechanisms.

POSITION → VELOCITY → ACCELERATION → INERTIAL FORCE → CONSTRAINT REACTION

  [Where is it?]  →  [How fast?]  →  [How fast is it changing?]  →  [F = m·a]  →  [Joint reactions for FEA]

  Kinematics:  POSITION → VELOCITY → ACCELERATION
  Dynamics:    ACCELERATION → INERTIAL FORCE → CONSTRAINT REACTION

When Kinematics Alone Is Sufficient

There are legitimate cases where a kinematic analysis is all that is needed, without a full dynamic solution. Mechanism synthesis — designing a linkage to achieve a desired output path — is a kinematic problem. Verifying that a mechanism does not interfere with surrounding structure throughout its travel is a kinematic problem. Checking that a control system has the required travel range is a kinematic problem. In each of these cases, the question is about geometry and motion, not about load. The error arises not from using kinematics but from assuming that kinematic results are sufficient when loads are needed.

• Mechanism synthesis — designing a linkage to trace a desired path is purely kinematic
• Clearance and interference checks — does the mechanism foul surrounding structure? — need only position
• Travel range verification — confirming required output displacement is kinematic
• Animation and visualisation — showing mechanism motion for review is kinematic
• None of the above produces the loads needed for structural assessment

Why a Static Position Analysis Cannot Replace a Dynamic Analysis

A static position analysis — sometimes called a quasi-static or kinetostatic analysis — computes the equilibrium of a mechanism at a given position, assuming the mechanism is moving slowly enough that inertial forces are negligible. This can be a useful first approximation for slowly moving mechanisms. However, for any mechanism that accelerates significantly — a rapidly deploying flap, a landing gear extension, a latch mechanism snapping into position — the inertial forces are not negligible and may dominate the load. A static position analysis at the same geometric configuration will miss these inertial contributions entirely, producing reactions that can be orders of magnitude lower than the real dynamic loads.

ASSUMING THAT A STATIC POSITION ANALYSIS CAN REPLACE A DYNAMIC ANALYSIS FOR A MECHANISM THAT ACCELERATES MISSES THE INERTIAL LOADS THAT OFTEN DOMINATE. Position alone does not determine load.

Forward Dynamics vs Inverse Dynamics

There are two ways to solve the dynamics problem, and the distinction matters for how loads are obtained. In forward dynamics, the applied forces and moments are known, and the solver integrates the equations of motion to predict the resulting motion and reactions. In inverse dynamics, the motion is prescribed (from kinematics or measurement), and the solver computes the forces and moments required to produce that motion. Both produce joint reactions. Forward dynamics is used when the motion is not known in advance — for example, a mechanism released from rest under spring force. Inverse dynamics is used when the motion is known — for example, a control surface driven through a prescribed deflection profile. The choice depends on what is known and what must be predicted.

Verification

When a dynamic analysis has been performed, the results should be checked for consistency between the kinematic and dynamic quantities. The accelerations from the dynamic solution should match those implied by the motion, and the forces should balance correctly at every time step.

• Check that the acceleration output from the dynamic solver is consistent with the velocity and position output — Numerically differentiate position and velocity and compare
• Verify that joint reactions balance the applied and inertial forces at each time step — Sum of forces and moments on each body should equal m·a and I·α
• Compare dynamic reactions against a static analysis at a slow-motion point to confirm they converge — At near-zero acceleration, dynamic should approach static
• Check that energy is conserved or dissipated as expected — In an undamped system, total energy should be constant; in a damped system, it should decrease

Key Takeaways

• Kinematics describes the geometry of motion; dynamics adds the forces that produce or result from that motion
• Knowing the position of a mechanism does not tell you the load without knowing how it is moving
• A dynamic analysis is required to produce the joint reactions needed for structural assessment
• A static position analysis misses the inertial loads that often dominate in rapidly accelerating mechanisms
• Forward dynamics predicts motion from forces; inverse dynamics computes forces from prescribed motion — both produce reactions