Calculator Directory
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Calculator 1
TOYO Sizing Software
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Calculator 2
Motion Profile Calculator
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Calculator 3
Actuator Loading & Moments
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Calculator 4
Linear to Rotary Converter
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Calculator 5
Load Inertia & Sizing Ratio
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Calculator 6
Bearing & Ball Screw Life
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Calculator 7
Motor Power & Electrical Demand
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Calculator 8
Product Selection Filters
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Sizing Motors & Drives for Linear Actuators

Selecting the optimal combination of linear actuators, mechanical drivetrains, and servo motors requires a balanced understanding of kinematic acceleration, steady-state thermal loads, and reflected dynamic inertia. Undersizing leads to positional lag, motor overheating, tracking errors, or premature bearing failure. Oversizing increases system inertia, drives up cabinet footprint, and needlessly inflates automation bill-of-materials costs.

A rigorous electric motion sizing workflow systematically addresses four foundational mechanical criteria:

  1. Kinematic Motion Profiling: Evaluating trapezoidal versus triangular velocity profiles to minimize required peak velocity, acceleration torque, and mechanical jerk during point-to-point moves.
  2. Guideway Loading & 3-Axis Moments: Quantifying normal loading (FN) and moment limits (Roll Mx, Pitch My, and Yaw Mz) induced by center-of-gravity offsets, mounting inclination angles, and dynamic deceleration.
  3. Linear-to-Rotary Conversion: Equating linear thrust and velocity to motor shaft speed (RPM) and torque (N·m or lb·in), while factoring in mechanical efficiency and gearbox reduction ratios.
  4. Reflected Load Inertia & Mismatch Tuning: Calculating reflected load inertia (Jload) at the motor shaft and maintaining an ideal inertia mismatch ratio (JL : JM ≤ 10:1) to guarantee rapid servo loop tuning and zero mechanical resonance.

Below is the TOYO Engineering Motion Suite, developed to provide automation integrators, machine builders, and mechanical design engineers with instantaneous, field-tested sizing calculations across both Metric (SI) and American Imperial units.

Calculator 1

Official TOYO Sizing Software

Cloud Actuator & Linear Motor Sizing Engine

TOYO's official cloud sizing software provides an interactive, comprehensive environment for sizing single-axis and multi-axis Cartesian systems across TOYO's complete portfolio of ball screw actuators, belt-driven modules, rack and pinion drives, and ironcore direct-drive linear motors.

The web application models your application's complete duty cycle, stroke profiles, payload masses, orientation angles, and operating environments. It evaluates critical ball screw whip speeds, guideway dynamic moments, thermal motor ratings, and expected actuator service life (km or hours), outputting verified engineering selection reports and recommended motor/drive packages.

Notice: Leaving TOYO Robotics Americas Clicking "Launch TOYO Sizing Software" will direct you to TOYO's factory web sizing application hosted on toyorobot.com/Select. The tool opens in a secure new browser tab so you can retain your session on this engineering portal.
Launch TOYO Sizing Software
TOYO Sizing Engine
Cloud-Based Sizing Highlights
  • Actuators & Linear Motors: Multi-axis Cartesian and single-axis evaluation
  • Duty Cycle Profiling: Acceleration, dwell times, and payload CoG offsets
  • Life & Safety Factors: Dynamic bearing life, critical speed, and thermal checks
  • PDF Engineering Report: Exportable sizing reports for project archives
Calculator 2

Motion Profile Calculator

Velocity & Acceleration Dynamics

Calculate the required linear acceleration, deceleration, and peak velocity for point-to-point moves. Compare a 1/3 Trapezoidal move, a Triangular move (zero flat dwell), and an optional Custom Accel/Decel move with results presented in dedicated tabs with copyable summaries.

Total point-to-point travel distance.
seconds (s)
Total allowable move execution time from start to stop.
Enable to input specific ramp times for asymmetric or custom constant-velocity motion.
Calculator 3

Actuator Loading & Moment Calculator

Thrust, Normal Load & Moments

Evaluate worst-case kinematic and static loads on your linear actuator. Calculate maximum thrust required, normal loading, and 3-axis moment loads (−Roll \(M_x\), Pitch \(M_y\), and Yaw \(M_z\)) based on mounting inclination angle, payload mass, acceleration, process forces, and center of gravity (CoG) offsets.

Sets payload, dimension, thrust, and moment measurement units.
° (0° to 90°)
0° (Pure Horizontal) 45° (Incline) 90° (Pure Vertical)
kg
Total mass of moving payload tooling, parts, and brackets.
m/s²
Equivalent G-force: 0.00 G
N
External continuous processing load (e.g. cutting, dispensing tip drag, insertion).
μ (0 to 1)
Profile rail recirculating linear bearings typically μ ≈ 0.03. Bushings ≈ 0.15 to 0.30.
Payload Center of Gravity (CoG) Lever Arm Offsets
Reference datum: Carriage Center Point
Rodless Actuator Coordinate Reference Hover or focus an input below to highlight its axis
Along travel stroke direction (+ forward / − rear)
mm
Generates Pitch Moment (My) with normal load.
Perpendicular horizontal offset (+ right / − left)
mm
Generates Roll (Mx) & Yaw (Mz) twisting.
Height / elevation above carriage mounting plane
mm
Increases Pitch (My) during acceleration & deceleration.
Accounts for friction surges, lubrication variations, and drive wear.
Calculator 4

Linear to Rotary Motion Calculator

Kinematic & Dynamic Conversion

Determine the required rotary motor shaft speed and output torque based on your actuator's linear travel velocity, axial thrust requirement, drive mechanism lead / pulley travel, and optional gear reduction.

Pre-sets mechanical efficiency ηmech for common linear transmissions.
%
Mechanical efficiency of the actuator transmission.
Maximum or rated operational travel speed.
Total axial thrust force required (including payload friction & acceleration).
mm / rev
Ball screw lead (lead per 360° revolution) or belt pulley linear travel per revolution (π × pitch diameter). Length unit automatically tracks with linear speed.
Check to include an inline speed reducer, planetary gearbox, or timing belt wrap ratio.
Calculator 5

Load Inertia & Motor Sizing Ratio Calculator

Reflected Inertia & Servo Sizing Ratio

Calculate the total reflected load inertia at the motor shaft and evaluate the critical inertia mismatch ratio (Jload : Jmotor) for ball screw and belt-driven linear actuators. Maintain servo control loop stability, prevent mechanical resonance, and optimize dynamic acceleration rates.

Mass of tooling, parts, or workpieces carried by the actuator.
Tare mass of the linear stage moving carriage block.
Ball Screw Material Preset: Carbon Steel (ρ = 7,850 kg/m³) Rotary screw inertia calculated automatically from solid cylinder geometry.
Linear travel per full turn of the screw.
Nominal outer diameter of the ball screw shaft.
Total shaft length (or stroke + ~150 mm end margins).
Check to include an inline planetary speed reducer, belt wrap ratio, or flexible coupling. Defaults to 1:1 direct coupling if unchecked.
Leave blank if unknown to view reflected load inertia only (Jload). Enter a value to evaluate the load-to-rotor inertia mismatch ratio (JL : JM).
Calculator 6

Bearing & Ball Screw Dynamic Life Calculator

ISO L10 Rated Life

Calculate the nominal 90% statistical reliability dynamic fatigue life (L10) of linear guideway bearings, rotary ball/roller bearings, and precision ball screws according to ISO standards. Evaluates total travel distance (km, m, miles), total revolutions, and elapsed operational service life (hours, days, years) under continuous or intermittent duty cycles.

1. Bearing Configuration, Dynamic Load Rating & Operating Payload
ISO dynamic rating based on 100 km nominal travel distance standard
Total moving payload mass or applied equivalent dynamic load
N
Direct moving payload or equivalent dynamic load acting during operation.
fw = 1.0
Service shock, vibration, and cyclical impact derating
1.0 1.5 2.0 2.5 3.0
Smooth operation with no external vibration
Calculate service life in operating hours, working days, and calendar production years based on your travel velocity and operating duty cycle. (Leave unchecked for instant distance-only / revolutions results).
Calculator 7

Motor Power & Electrical Demand Calculator

Drive Power & Electrical Demand

Calculate the mechanical output power (Watts and HP), required electrical input power, and continuous operating phase and DC bus current draw for servo motors, stepper systems, and direct-drive linear motors. Use this module to size amplifier drive current ratings, DC power supply wattage, and thermal drive envelopes.

1. Operating Point (Torque/Force & Velocity)
Continuous running or peak acceleration torque
Direct shaft torque required from motor sizing.
Rotational velocity during movement
Operating speed sustained under required torque.
2. Motor & Electrical Bus Parameters
Standard DC bus or rectified AC supply
Bus voltage available at the motor amplifier.
Electromechanical torque-to-current ratio
From manufacturer motor datasheet.
Mechanical & drive conversion efficiency
%
Typically ~90% for ball screws, ~88% for belt drives, ~95% for linear motors.
Calculator 8

Product Selection Filters

Multi-Parameter Actuator & Drive Selection Engine

Rapidly narrow down TOYO's complete catalog of linear actuators, electric cylinders, multi-axis gantry robots, and direct-drive linear motors using our interactive multi-parameter engineering filters.

Filter and match real-time industrial mechanisms across required stroke length (up to 5,000 mm), maximum travel velocity (up to 5,000 mm/s), positional repeatability (±1 µm to ±100 µm), drivetrain architecture (ball screw, timing belt, linear motor), environmental cleanroom rating (Class 10 / ISO 4), and integrated motor/drive options.

Launch Product Selection Filters
TOYO Product Selection Filters
Interactive Filter Capabilities
  • Travel & Velocity Sliders: Instant multi-axis weeding
  • Sub-Micron Precision: Repeatability threshold tuning
  • Drivetrain Types: Ball Screw, Belt, & Linear Motor
  • Cleanroom & Motor Filters: ISO 4 and turn-key package options

Engineering Formulas & Conversion Principles

Rotary Speed from Linear Velocity

The relationship between linear velocity v and mechanism rotational speed Nmech is determined by the linear distance per revolution p (lead or pulley pitch circumference):

N_mech (RPM) = (v / p) × 60

When a speed reduction gear ratio i is present (e.g. i = 4 for a 4:1 reducer), motor shaft speed becomes:
N_motor = N_mech × i

Rotary Torque from Linear Thrust

Required input torque is derived by equating linear work to rotary work while accounting for system mechanical efficiency η:

T_mech = (F × p) / (2 × π × η_mech)

Factoring in a gearbox with ratio i and gear efficiency ηgear, the required motor shaft torque is:
T_motor = T_mech / (i × η_gear)

Trapezoidal Move Profile (1/3 - 1/3 - 1/3)

Equally divides total move time T into acceleration, constant velocity, and deceleration segments (tacc = tdec = tflat = T / 3):

V_max = 1.5 × (s / T) = 1.5 × V_avg
Accel = Decel = V_max / (T / 3) = 4.5 × s / T²
Triangular Move Profile (Zero Dwell)

Smooth acceleration and deceleration with zero constant speed cruise (tacc = tdec = T / 2), yielding minimum acceleration for a given time but higher peak speed:

V_max = 2.0 × (s / T) = 2.0 × V_avg
Accel = Decel = V_max / (T / 2) = 4.0 × s / T²
Actuator Axial Thrust Mechanics

Net axial drive force sums gravitational weight along stroke, guideway friction, and inertial acceleration:

F_N = m × g × cos(θ)
F_thrust = (m × g × sin(θ)) + (μ × F_N) + (m × a) + F_ext
F_thrust,max = F_thrust × Safety_Factor
3-Axis Dynamic Moment Loading

Moments are evaluated around carriage guideway centers based on payload Center of Gravity (CoG) lever arms:

Pitch (M_y) = |F_N × L_x| + |(F_accel + F_g + F_ext) × L_z|
Roll (M_x) = |F_N × L_y|
Yaw (M_z) = |(F_accel + F_ext) × L_y|
Reflected Linear Mass & Screw Inertia

Linear mass reflects to rotational inertia via the radius conversion constant R = Lead / (2π) or Dp / 2. Ball screw solid cylinder inertia is governed by the 4th power of radius:

J_linear = m_total × R²
J_screw = (π × ρ_steel × L × r&sup4;) / 2
Gearbox Reflected Ratio & Mismatch Sizing

A speed reducer attenuates total mechanism inertia by the square of its ratio (i²), bringing the final mismatch ratio into the ideal control band (≤ 10:1):

J_load,reflected = (J_shaft / i²) + J_gearbox + J_coupling
Inertia_Ratio = J_load,reflected / J_motor
ISO Rated Dynamic Fatigue Life (L₁₀)

Calculates the 90% survival life under applied operating load and operating condition factor (fw):

Linear Guideway: L_10 (km) = [ C_100 / (P × f_w) ]p × 100 km
Ball Screw Revs: L_10,rev = [ C_a / (F_a × f_w) ]³ × 10⁶ revs
Ball Screw Dist: L_10 (km) = (L_10,rev × p_lead) / 10⁶ km
Rotary Bearing: L_10 (10⁶ revs) = [ C_r / (P_r × f_w) ]p × 10⁶ revs

Where p = 3 for ball contact, p = 10/3 for roller bearings, and fw ranges from 1.0 (smooth) to 3.0 (high vibration/shock).

Operational Lifetime & Duty Cycle Sizing

Service life in hours and production calendar time is evaluated from average linear velocity v or rotational RPM N and duty cycle percentage:

Active Hours: L_10h = L_10 / (v × 3600)
Calendar Days = L_10h / (Duty_Cycle × Hours_Per_Day)
Calendar Years = Calendar_Days / Days_Per_Year
Mechanical & Electrical Input Power

Mechanical output power is evaluated from torque and angular speed (rotary) or thrust and linear velocity (linear). Electrical input power accounts for actuator and drivetrain mechanical efficiency (η):

Rotary Mech Power: P_mech (W) = [τ (N·m) × N (RPM)] / 9.5488
Linear Mech Power: P_mech (W) = F (N) × v (m/s)
Mechanical HP = P_mech / 745.7
Electrical Input Power: P_elec (W) = P_mech / η
Operating Current Draw & DC Bus Demand

Operating phase current is derived directly from motor torque constant (Kt) or force constant (Kf). Supply DC bus current accounts for electrical conversion power:

Motor Phase Current: I_phase (A) = τ (N·m) / K_t (N·m/A)
Linear Phase Current: I_phase (A) = F (N) / K_f (N/A)
DC Bus Current: I_bus (A) = P_elec (W) / V_bus (VDC)

Where rectified single-phase bus: VDC ≈ VAC × √2, and rectified 3-phase bus: VDC ≈ VAC × 1.35 to 1.41.