Accurate kinematic and dynamic conversion between linear actuation and rotary motors is fundamental to sizing precision automation systems. Whether you are specifying a high-speed belt drive, a high-thrust ball screw, or a compact lead screw stage, matching the linear load requirements to the motor shaft parameters ensures optimal dynamic performance, thermal stability, and mechanical reliability.

Below you will find dedicated engineering calculators developed to streamline your sizing and verification workflow. Each calculator operates independently and provides structured, copy-ready results for your engineering documentation.

Calculator Directory
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Calculator 1
Motion Profile Calculator
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Calculator 2
Actuator Loading & Moments
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Calculator 3
Linear to Rotary Converter
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Calculator 1

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 2

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 3

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.

Engineering Formulas & Conversion Principles

Rotary Speed from Linear Velocity

The relationship between linear velocity \(v\) and mechanism rotational speed \(N_{mech}\) 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 \(\eta\):

T_mech = (F × p) / (2 × π × η_mech)

Factoring in a gearbox with ratio \(i\) and gear efficiency \(\eta_{gear}\), 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 (\(t_{acc} = t_{dec} = t_{flat} = T/3\)):

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 (\(t_{acc} = t_{dec} = T/2\)), 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|