Size motors and determine feasible axis motion
Model DC motor torque and speed, estimate servo RMS and peak load, and test point-to-point motion-time feasibility.
Engineering calculators
Mechatronics & Robotics Calculators
Estimate motor torque and speed, servo duty, positioning accuracy, tracking error and control-loop feasibility for electromechanical systems. Connect motion demands with drive limits, sensing quality and controller behavior before relying on a performance estimate.
Find your calculation path
Start with the engineering problem
Choose the check or decision you need to make, then open the appropriate calculator.
Assess tracking, synchronization and positioning
Screen servo following error, electronic cam/gearing lag and settling or positioning accuracy requirements.
Check control-loop bandwidth and sensor data
Compare sample rate and delay with crossover bandwidth, and quantify fusion uncertainty for two correlated sensors.
Obtain initial PID controller settings
Compare Cohen–Coon and Ziegler–Nichols FOPDT tuning with ultimate-gain/oscillation-based Ziegler–Nichols settings.
Calculator library
All Mechatronics & Robotics Calculators
Browse the complete set of published tools in this engineering category.
Cohen–Coon PID Tuning Calculator — Kp, Ki, Kd for FOPDT Processes
Calculate P, PI or PID controller settings from signed process gain, time constant and dead time, including Kp, Ki, Kd, Ti, Td, L/T…Control Loop Bandwidth Feasibility Calculator — Phase Margin, Sampling & Delay
Check a target gain-crossover frequency against sampling rate, digital delay, required phase margin and an optional first mechanical resonance, with estimated phase margin,…DC Motor Torque & Speed Calculator — Back EMF, Stall Current & Power
Calculate DC motor developed torque and steady-state speed from armature current, supply voltage, armature resistance and Kt/Ke, with back EMF, copper loss, converted…Electronic Cam & Electronic Gearing Calculator — Tracking Lag, Max Speed & Servo Bandwidth
Estimate master–slave position tracking lag for electronic gearing or camming, then determine allowable master speed or minimum equivalent servo bandwidth from angular-error tolerance…Motion Profile Calculator — Minimum Move Time & Feasibility Check
Check whether a point-to-point move can meet its target time using symmetric trapezoidal or jerk-limited S-curve motion limits, with minimum move time, peak…PID Tuning Calculator — Ziegler–Nichols FOPDT Method for Kp, Ki and Kd
Ziegler–Nichols PID tuning calculator for P, PI and PID controllers using a FOPDT process model with process gain K, time constant T and…Sensor Fusion Uncertainty Calculator — Correlated Two-Sensor BLUE & Fusion Gain
Calculate 1σ fused uncertainty for two unbiased length sensors using correlated BLUE weighting, with fusion gain plus optional latency, paired sampling-rate and uncertainty-requirement…Servo Following Error & Position Loop Gain Calculator
Estimate servo tracking error for constant-velocity or acceleration-ramp motion, size the minimum ideal position-loop gain, and screen velocity feedforward and loop-bandwidth separation.Servo Motor Sizing Calculator — RMS & Peak Torque, Duty Cycle
Estimate servo RMS torque, required peak torque, thermal utilization and inertia ratio from load inertia, gearing, motion timing and candidate motor ratings.Servo Positioning Accuracy & Settling Time Calculator
Check whether a closed-loop servo axis can meet a positioning accuracy and settling-time requirement from move distance, allowed time, −3 dB bandwidth, damping…Ziegler–Nichols PID Tuning Calculator — Kp, Ki, Kd from Ultimate Gain Ku and Oscillation Period Tu
Calculate classic Ziegler–Nichols P, PI and PID tuning settings from ultimate gain Ku and ultimate oscillation period Tu, including Kp, Ki, Kd, Ti…Engineering context
Choosing the right level of verification
When a calculator is sufficient
Use focused mechatronics calculators to screen feasibility after defining the physical axis, actuation technology, motion requirements and available sensor data.
- Convert mechanical load and inertia consistently to the motor shaft before selecting motor and gearbox ratings.
- Distinguish peak torque, continuous/RMS torque and short-term drive current limits.
- Use realistic closed-loop bandwidth and damping estimates when evaluating response time or following error.
- For PID or synchronization screening, document the process model, controller structure, delays and measurement assumptions.
When to extend the analysis
Move to full electromechanical modeling and testing when servo dynamics, thermal behavior or coupled axes dominate performance.
- Validate motor and drive combinations against manufacturer torque–speed envelopes, thermal limits and regenerative operating regions.
- Use identified plant models and closed-loop simulation for delay, resonance, saturation, nonlinear friction and disturbance rejection.
- Check encoder quantization, sensor synchronization, electrical noise, wiring and safety functions independently.
- For production motion systems, test positioning, settling, repeatability and fault response under representative loads and temperatures.
Common assumptions and mistakes
- Using peak torque as a continuous rating: A motor may meet peak demand but overheat during repetitive motion; RMS torque and actual duty matter.
- Assuming ideal transmission behavior: Backlash, compliance, gearbox loss and reflected inertia can alter accuracy and stability.
- Confusing resolution with accuracy: Encoder counts do not alone establish actual mechanical positioning accuracy.
- Treating PID formulas as final commissioning values: Tuning rules are starting estimates; plant identification, robustness and safety checks remain necessary.
- Ignoring control delays: Communication and sampling delays can impose tighter bandwidth and phase-margin limits than the nominal mechanical model.
Engineering questions
Frequently asked questions
What should I calculate first when selecting a servo motor?
Begin with motion profile, load inertia and required peak/continuous torque. Then compare the manufacturer torque–speed curve, drive current, gearbox characteristics and thermal duty cycle.
How does RMS torque differ from peak torque?
Peak torque relates to the maximum instantaneous motion or load event. RMS torque represents the heating-equivalent duty over the modeled cycle and is central to continuous thermal sizing.
Does high encoder resolution guarantee precise positioning?
No. Resolution is only one contribution; mechanical compliance, backlash, sensor errors, control response, thermal changes and repeatability also affect delivered accuracy.
Can a PID calculator fully tune a real machine?
No. Cohen–Coon and Ziegler–Nichols methods give starting parameters based on particular models or tests. Actual control performance requires commissioning, stability assessment and validation.
Why is control-loop bandwidth limited by mechanical resonance?
A controller that reacts too quickly near structural resonance can amplify oscillations and reduce stability margin. Sampling, delay and noise can constrain usable bandwidth as well.
What does electronic-cam phase error mean?
It is the estimated angular mismatch between a commanded master/slave relationship and the modeled slave response. Real performance additionally depends on axis dynamics, feedback and controller implementation.
Can sensor fusion always improve measurement uncertainty?
No. The two-sensor BLUE calculation depends on unbiased measurements and the supplied uncertainties and correlation. Highly correlated measurements or unsuitable assumptions may limit the improvement. Latency and sampling constraints require separate review.
Does servo motor sizing prove the axis will meet settling-time requirements?
No. The servo motor sizing tool checks estimated RMS and peak torque, thermal utilization and inertia ratio. Positioning accuracy, closed-loop bandwidth, tracking error and settling time are distinct checks covered by other tools in this category.