Establish linear and rotational motion requirements
Solve constant-acceleration translation, rotational torque and speed, and jerk-limited move-time constraints.
Engineering calculators
Kinematics & Dynamics Calculators
Analyze linear and rotational motion, acceleration, stopping distance, motion-profile feasibility and resonance separation for moving machinery. Use the right kinematic model first, then include inertia, drive limits and dynamic loading where the design requires them.
Find your calculation path
Start with the engineering problem
Choose the check or decision you need to make, then open the appropriate calculator.
Check machine throughput and synchronized paths
Estimate cycle time, coordinate two moving axes, and test cornering speed against acceleration and jerk limits.
Analyze stopping and positioning performance
Estimate stopping distances, deceleration demand and the time and residual error for a damped settling axis.
Screen cam and rotating-system dynamic risks
Analyze cam follower contact and motion limits, then screen rotating excitation against natural frequency and critical speed.
Calculator library
All Kinematics & Dynamics Calculators
Browse the complete set of published tools in this engineering category.
Axis Settling Time & Positioning Accuracy Calculator
Calculate total stop-and-settle time and residual positioning error for a damped axis model using equivalent mass, stiffness, damping ratio, stop velocity, deceleration, allowed…Cam Follower Calculator — Motion, Contact Force & Pressure Angle
Analyze a radial roller cam follower from lift, motion law, cam speed, follower mass, spring data and geometry to calculate acceleration, contact force,…Constant Acceleration Calculator — Velocity, Acceleration, Time & Displacement
Enter any three of initial velocity, final velocity, acceleration and elapsed time to solve the fourth; displacement, average velocity and reversal-point results are…Critical Speed & Natural Frequency Calculator — Resonance Separation Margin
Calculate the natural frequency and critical speed of an equivalent stiffness–mass system, then screen 1×, 2×, gear-mesh or external cyclic excitation for resonance…Jerk-Limited S-Curve Motion Profile Calculator
Calculate a jerk-limited S-curve motion profile: find minimum move time from distance, velocity, acceleration and jerk limits, or calculate the required peak velocity,…Machine Cycle Time Calculator — Throughput & Motion Feasibility
Calculate minimum machine cycle time and maximum cycle rate from stroke, velocity, acceleration and dwell limits, with one-way or reciprocating motion and target-time…Multi-Axis Synchronized Motion Calculator — Minimum Time & Following Error
Calculate the minimum synchronized move time for two axes from travel, velocity and acceleration limits, validate a target move time, and optionally check…Path Cornering Speed Calculator — Radius, Lateral Acceleration & Jerk Limits
Evaluate commanded path speed against corner radius, lateral acceleration and normal jerk limits, with speed reduction, utilization, effective radius and feasibility results.Rotational Motion Calculator — Angular Acceleration, Required Torque & Power
Calculate constant-acceleration rotational motion from initial and final angular speed using either time or angular acceleration, with optional shaft torque, work, power, torque-capacity…Stopping Distance Calculator — Braking Distance, Required Deceleration & Traction Limits
Calculate total stopping distance and time from known deceleration, solve the deceleration required within an available distance, or evaluate a friction- and grade-limited…Engineering context
Choosing the right level of verification
When a calculator is sufficient
Use a focused motion calculator when the initial conditions, motion law and performance target are clear. Start by distinguishing position, velocity and acceleration from the forces or torques that generate the motion.
- Use a constant-acceleration model only when the acceleration history can reasonably be represented by one constant value.
- For rotational motion, supply appropriate equivalent inertia and distinguish shaft load torque from motor-side torque.
- For stopping, include the time or distance before deceleration begins, not merely the nominal braking phase.
- For resonant-speed screening, document the mass, stiffness, excitation order and operating-speed range.
When to extend the analysis
Detailed motion and dynamics verification becomes necessary when loads are time-dependent, coupled or safety-critical.
- Model multi-axis coordination, structural compliance, backlash and drivetrain elasticity when positioning accuracy is important.
- Check real motor torque–speed curves, thermal duty, regenerative braking and inertia reflected through gears or screws.
- Use a multi-degree-of-freedom model, modal testing or FEA where one equivalent stiffness and mass is insufficient.
- Include emergency stops, friction variation, jerk constraints and mechanical impact loads in machine-safety assessments.
Common assumptions and mistakes
- Conflating kinematics and dynamics: A motion equation describes the path, not necessarily the force or torque required to follow it.
- Ignoring sign conventions: Direction reversal, negative acceleration and signed angular displacement must be interpreted consistently.
- Using a peak value as a duty-cycle estimate: Peak torque does not replace RMS torque, energy, heating or cycle-time analysis.
- Equating nominal stopping distance with safety clearance: Sensor delay, controller delay, brake response, variation and the governing safety methodology still matter.
- Treating simplified resonance margins as certification: A single-degree-of-freedom screen cannot identify all structural modes or excitations.
Engineering questions
Frequently asked questions
What is the difference between kinematics and dynamics?
Kinematics determines motion quantities such as position, velocity and acceleration. Dynamics adds forces, moments and inertia to explain or predict how that motion is produced.
When is a constant-acceleration model appropriate?
Use it when acceleration is adequately approximated as constant over the interval. Servo ramps, jerk limits and discontinuous or nonlinear motion may require a piecewise or time-domain model.
How do I estimate acceleration torque for a rotating axis?
Use Rotational Motion with an appropriate moment of inertia, angular acceleration and any signed load torque. Then review gearing, efficiency and motor torque capacity separately.
Does stopping distance include reaction or control delay?
The Stopping Distance tool accounts for modeled reaction delay in addition to the braking phase. Actual stopping systems must also consider measured hardware response and relevant safety requirements.
Why does jerk matter in motion planning?
Jerk is the rate of change of acceleration. Limiting it can reduce abrupt load changes and excitation, but it may increase move time and can require more complex profiles.
Does a critical-speed check identify every resonance?
No. A simplified natural-frequency or critical-speed assessment screens defined excitations in an equivalent model. Additional modes, structural flexibility and harmonics may require modal analysis or testing.
When is a jerk-limited S-curve preferable to a constant-acceleration calculation?
Use the jerk-limited motion-profile calculator when acceleration transitions matter for motion feasibility. It evaluates velocity, acceleration and jerk constraints and can solve minimum move time or the limits required for a target move time. Actual drive torque and structural response need additional checks.
Does the multi-axis synchronization calculator predict servo following error?
It determines kinematic move-time feasibility for two axes and can compare an entered measured peak following error with an allowable limit. It does not independently predict a servo system’s closed-loop tracking behavior from controller parameters.