Trajectory Planner: Trapezoidal Velocity Profile

Designing smooth motion for a linear actuator or robotic joint isn’t just about picking a speed—you have to plan out acceleration, cruising, and deceleration if you want to avoid jarring movements and overshooting your stop. The calculator on this page lets you work out acceleration time, cruise time, deceleration time, and total move time based on your move distance, max velocity, and max acceleration. In real shop-floor applications—CNC, robotics, actuator controls—a sloppy move profile leads to wear, missed steps, or unfinished cycles. Below you’ll find all the formulas, a step-by-step worked example, practical notes, and answers to regular engineering questions.

What is a Trapezoidal Velocity Profile?

A trapezoidal velocity profile ramps your system up to speed in a controlled way, keeps it moving at a set velocity, then slows it down smoothly at the end. If you plot velocity versus time, it forms a shape with straight sides and a flat top—hence the name.

Simple Explanation

Imagine you’re getting onto a motorway: you gradually accelerate, cruise at highway speed, and then slow down for your exit. That’s exactly the approach this applies to an actuator—control the ramp up, hold steady, and then ramp down carefully. The goal is to avoid sudden stops or starts that can harm your mechanism.

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Trapezoidal Velocity Profile Diagram

Trapezoidal Velocity Profile Calculator

How to Use This Calculator

1. Enter your total move distance in the Total Distance field (mm or inches).
2. Enter the top speed your system is allowed to reach in the Maximum Velocity field.
3. Enter the maximum rate of speed change in the Maximum Acceleration field.
4. Click Calculate to see your result.

📹 Video Walkthrough — How to Use This Calculator

Mathematical Equations

Complete Guide to Trapezoidal Velocity Profiles

Simple Example

Distance: 50 mm, Maximum Velocity: 10 mm/s, Maximum Acceleration: 5 mm/s²

• Acceleration time: 10 / 5 = 2.0 s
• Acceleration distance: ½ × 5 × 2² = 10 mm each way (20 mm total)
• Cruise distance: 50 − 20 = 30 mm
• Cruise time: 30 / 10 = 3.0 s
• Total time: 2.0 + 3.0 + 2.0 = 7.0 s

Understanding Motion Control Fundamentals

The calculator is rooted in real motion planning—you’ll see this approach in most automation and robotic setups using FIRGELLI linear actuators. It works by splitting the move into three blocks: a ramp up, a steady cruise, and a ramp down, all calculated from simple kinematics—no more, no less.

Plain on-off moves are rough. If you want parts to last or positions to be accurate, you need a controlled profile. Trapezoidal profiles handle that by smoothing the transition at start and end, so you’re not hammering the mechanism every time it changes direction or speed.

The Physics Behind Velocity Profiling

The trapezoidal name comes from its time-velocity plot: it accelerates at a set rate, sits at a constant velocity as long as it can, then slows down with the same rate. Each block is governed by the basic equations of motion—no fancy math needed. That’s enough to plan trajectories accurately and prevent sudden shocks in your real hardware.

Position is just the area under the velocity curve. Control the shape of that curve, and you control the whole move—nothing more to it. This keeps calculations reliable and hardware behavior predictable, which is what matters out in the field.

Practical Applications in Automation

You’ll find this velocity profile in most industrial automation: CNC tools use it to keep cuts clean and tools alive longer, robot arms use it for smooth pick-and-place so delicate parts don’t bounce, and conveyors rely on it so stuff doesn’t jump or jam at starts and stops.

Anywhere you’ve got a linear actuator—solar tracking, machine tools, industrial valves—a proper move profile avoids backlash, reduces wear and tear, and simply makes the mechanism last longer between failures. It’s often the difference between reliable cycles and constant downtime.

Design Considerations and Constraints

Setting up a velocity profile in practice always comes down to physical limits. Acceleration is limited by what your motor or actuator can push, plus the inertia of whatever you’re moving. Go too high and you’ll either stall or overheat; too low and you slow the whole process down unnecessarily.

The speed limit is set by friction, load dynamics, maybe power supply headroom. It’s common to pick a velocity below absolute max for consistent performance, especially if your load can change.

Distance, velocity, and acceleration all tie together: if you don’t have enough distance, you simply can’t hit your requested top speed. For short moves, the calculator will show a triangular profile rather than true trapezoidal—you ramp up, and before you know it, you’re ramping down.

Worked Example: Linear Actuator Positioning

For context, here’s a real example: move a 5kg load with a linear actuator 200mm across. Let’s say your actuator can hit 50 mm/s and 100 mm/s² max.

Plug into the calculator:

• Distance: 200 mm
• Maximum velocity: 50 mm/s
• Maximum acceleration: 100 mm/s²

Results are:

• Acceleration time: t_a = 50/100 = 0.5 seconds
• Acceleration distance: d_a = ½ × 100 × 0.5² = 12.5 mm
• Total acceleration/deceleration distance: 25 mm
• Cruise distance: 200 - 25 = 175 mm
• Cruise time: 175/50 = 3.5 seconds
• Total time: 0.5 + 3.5 + 0.5 = 4.5 seconds

This keeps motion smooth and well within what your actuator can handle, and if you want to check limits or cycle time, you can tweak the numbers quickly.

Advanced Considerations

If your application is highly sensitive to vibration or resonance, more advanced profiles (S-curve/jerk limited) help by softening the snap at acceleration changes. Still, most industry setups stick to trapezoidal profiles since they’re easy to implement and do the job for the majority of machines.

If you’re synchronizing several axes—think multi-axis stages or robots—timing gets trickier. Each axis might have a different max velocity or acceleration, but you still want them starting and finishing at the same time. That usually means coordinating individual profiles, sometimes manually, sometimes in software.

For real-time control, check your controller’s calculation speed and servo loop rate. Your output from this calculator becomes the reference for the motion controller, which then breaks it into thousands of tiny time slices for the drive hardware.

Integration with Control Systems

When you run these calculations, the results feed straight into the motion controller. Most modern controllers interpolate these profiles at high speed (often 1 kHz or faster).

The motor controller or drive system constantly checks position and velocity, comparing real feedback to your profile. Any error gets corrected in real time. If you need high accuracy—say for chip manufacturing or fine assembly lines—you might run a feedforward controller as well, using the planned profile to anticipate loads and further reduce lag or overshoot.

Bottom line: well-planned motion profiles won’t magically fix poor mechanics, but they’ll get you as close as possible to what your actuator and controller are capable of, cycle after cycle.

Frequently Asked Questions

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