For engineers who already know the math—but still lose projects. For the last few years, I’ve been sharing technical guides here on Mechanical Design Handbook —how to size a motor, how to calculate fits, and (as you recently read) how to choose between timing belts and ball screws. But after 25 years in industrial automation, I realized something uncomfortable: Projects rarely fail because the math was wrong. They fail because: The client changed the scope three times in one week. A critical vendor lied about a shipping date (and no one verified it). The installation technician couldn’t fit a wrench into the gap we designed. University taught us the physics. It didn’t teach us the reality. That gap is why I wrote my new book, The Sheet Mechanic . This is not a textbook. It is a field manual for the messy, political, and chaotic space between the CAD model and the factory floor. It captures the systems I’ve used to survive industrial projec...
The Failure Scenario: You upgraded to linear rails. You tightened your belts. But when you print a calibration cube at 100mm/s, you see "echoes" (ripples) next to the letter X. This is Ghosting (or Ringing).
The Cause: This is a Resonance problem. Every machine has a "Natural Frequency" (fn)—like a guitar string. When your print head changes direction sharply, it "plucks" the frame. If the frequency of that pluck matches the frame's natural frequency, the machine vibrates uncontrollably.
The solution is not hardware—it is math. This guide explains how Input Shaping cancels these vibrations before they even start.
Table of Contents
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1. The Physics: Acceleration vs Jerk
To understand ghosting, you must understand the derivatives of position.
- Velocity: How fast you move (mm/s).
- Acceleration: How fast you change velocity (mm/s²).
- Jerk: How fast you change acceleration (mm/s³).
The Problem: When a printer reaches a corner, it must stop X and start Y. If it does this instantly (Infinite Jerk), the frame shudders.
Engineering Nuance: In classic Marlin firmware, "Jerk" is technically a velocity threshold (instant speed change), not true mathematical Jerk. However, the physical result is the same: instant direction changes excite vibration modes.
Figure 1: Ghosting (Left) looks like ripples in a pond. It happens after sharp corners. Input Shaping (Right) actively cancels these ripples.
2. The Magic: How Input Shaping Works
Input Shaping (in Klipper or Marlin) is basically Noise Canceling Headphones for your printer.
It doesn't make the frame stiffer. Instead, it sends a "counter-signal." If the firmware knows that a sharp corner will make the frame vibrate to the right, it commands a tiny jerk to the left milloseconds before the corner to cancel the wave.
Industrial Context: In professional CNC machines ($100k+ Datrons), this is called "Command Pre-Filtering" or S-Curve profiling. Your 3D printer is now using the same advanced control theory as high-end aerospace mills.
Figure 2: An ADXL345 Accelerometer measures the "Natural Frequency" of your X and Y axes (usually 40Hz - 60Hz). Input Shaping targets these specific peaks to kill vibration.
3. Tuning Guide: Accelerometer vs Manual
You have two ways to fix this:
Method A: The "ADXL345" (Scientific)
You mount a $5 accelerometer chip to your print head. The printer shakes itself at different frequencies (10Hz to 100Hz) and measures exactly where it resonates. Klipper then automatically generates the shaping graph.
Method B: The "Ringing Tower" (Manual)
You print a test tower where the acceleration increases every 5mm. You measure the distance between the ripples on the print with calipers.
Formula: Frequency = (Print Speed) / (Ripple Distance)
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4. Engineering Summary
The Fix Checklist:
1. Tighten belts to 110Hz (Use a phone app).
2. Switch firmware to Klipper if possible.
3. Install an ADXL345 Accelerometer to map resonance.
4. Enable Input Shaping to double your acceleration without ghosting.
1. Tighten belts to 110Hz (Use a phone app).
2. Switch firmware to Klipper if possible.
3. Install an ADXL345 Accelerometer to map resonance.
4. Enable Input Shaping to double your acceleration without ghosting.
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5. Common Questions (FAQ)
Q: Can I use Input Shaping on Marlin?
A: Yes, modern Marlin (2.1.2+) supports Input Shaping. However, it usually requires manual tuning (Ringing Tower) because it cannot easily read an USB accelerometer data like Klipper can.
Q: Does tightening belts fix ghosting?
A: It helps shift the frequency higher (making ripples smaller), but it cannot eliminate it. All belts act like springs. You need Input Shaping to mathematically cancel the spring effect.
Q: What is a good acceleration setting?
A: For a standard Ender 3 (Bed Slinger), 500mm/s² is safe, 1500mm/s² is the limit. With Input Shaping, you can push this to 3000mm/s². For CoreXY, 5000mm/s² to 10,000mm/s² is common.
🔧 The Complete Motion Control Series
This article concludes our deep dive into machine design. Review the full system:
- 1. Structure: Linear Rails vs Rods
- 2. Transmission: Timing Belts vs Ball Screws
- 3. Drive: NEMA 17 vs 23 (Torque & Speed)
- 4. Alignment: Oldham Couplers (Z-Wobble Fix)
- 5. Tuning: Ghosting & Input Shaping
You tuned the firmware. Now tune the project plan.
The Sheet Mechanic is the guide to the political, financial, and chaotic side of engineering that they didn't teach you in school.
About the Author:
This article is written by a mechanical design engineer specializing in industrial automation, sensor selection, and closed-loop control systems.
This article is written by a mechanical design engineer specializing in industrial automation, sensor selection, and closed-loop control systems.
As an Amazon Associate, I earn from qualifying purchases.
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