Skip to main content

Featured Post

Why I Wrote The Sheet Mechanic (And Why Calculations Aren’t Enough)

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...
Post a Comment
NEW RELEASE: Stop trying to be a Hero. Start being a Mechanic. Get "The Sheet Mechanic" on Amazon »

Chain Drive Formulas: Pitch, Length & Center Distance (Part 3)

Key Geometric Calculations

In Part 2, we analyzed the loads. Now, we must size the geometry.

Designing a chain drive involves a specific sequence: determining the sprocket size, estimating the center distance, calculating the required chain length in "pitches," and then recalculating the exact center distance.

Advertisement

1. Pitch Diameter

The pitch diameter is the theoretical circle that passes through the centers of the chain pins.

  • D1 = Pitch Diameter of Driver Sprocket (Small)
  • D2 = Pitch Diameter of Driven Sprocket (Large)
  • N1 = Number of Teeth on Driver
  • N2 = Number of Teeth on Driven
  • p = Chain Pitch
D1 =
p
sin( 180 / N1 )
Calculator Note:
Most calculators default to Degrees mode.
  • If using Degrees: Use 180 / N
  • If using Radians (e.g., Excel): Change 180 to Ï€ → sin(Ï€ / N)

2. Center Distance Guidelines

The Center Distance (C) is the distance between the shafts. While chains are flexible, sticking to standard design ranges ensures long life.

Engineering diagram showing chain drive center distance C, pitch diameters D1/D2 and contact angle theta

Figure 1: The geometry of a two-sprocket chain drive, defining the Center Distance (C) and Angle of Contact (θ).

  • Minimum: The sprockets must not touch. Ideally, C should be at least 30 to 50 times the pitch (30p - 50p).
  • Maximum: Long spans can cause vibration. If C > 80 pitches, guide rails or tensioners are recommended.

3. Chain Length Calculation

This is the most critical step. Unlike a belt, you cannot have a fraction of a chain link. The total length (L) must be an integer number of pitches.

The standard formula to approximate the length in pitches (L) based on a preliminary center distance in pitches (C) is:

L = 2C +
N2 + N1
2
+
(N2 - N1)2
4 π2 C
Advertisement

Design Rule of Thumb:

"It is preferable to have an odd number of teeth on the driving sprocket and an even number of pitches (links) in the chain. This prevents a specific link from constantly engaging the same tooth, distributing wear evenly."

4. Exact Center Distance Recalculation

Once you calculate the chain length, you must round it to the nearest even integer. Because you changed the length, you must now calculate the exact center distance to mount your motor correctly.

This formula calculates the Center Distance in standard units (mm or inches), where p is the pitch:

C =
p
8
[ 2L - (N2 + N1) + √[2L - (N2 + N1)]2 - 0.81(N2 - N1)2 ]

5. Angle of Contact

Finally, verify that the chain wraps sufficiently around the small sprocket. The arc of contact (θ) should ideally be greater than 120° to prevent teeth jumping (ratcheting).

θ = 180° -
2 (D2 - D1)
C
× 60

References

  • Robert L. Mott, Machine Elements in Mechanical Design
Labels:

Comments

Post a Comment
Disclosure: As an Amazon Associate, I earn from qualifying purchases.

Popular posts from this blog

Dowel Pins & Locating Pins: The Basics of Fixture Design

Figure 1: A typical fixture setup. Notice how dowel pins (silver) provide precise location, while bolts (not shown here) provide the clamping force. In the world of Precision Engineering , the difference between a high-quality product and a scrap part often comes down to microns. While bolts hold parts together, they are terrible at positioning them. This is where Dowel Pins and Locating Pins become essential components in industrial tooling . Advertisement What is a Dowel Pin? Dowel pins are precision-ground fasteners used to secure the relative position of two parts. They are typically machined to extremely tight tolerances (often within 0.0001 inches) and are available in materials like: Hardened Steel: For high-wear applications in CNC fixtures . Stainless Steel: For corrosion resistance in medical or food processing machinery. Plastic (Thermoplastic): For lightweight, non-conductive, low-load alignment. The ...
Post a Comment
Read more about this Mechanical Design Article »

Engineer's Guide to Ball Detent Torque Limiters

Figure 1: The ball detent mechanism provides precise overload protection by disengaging instantly when the torque limit is exceeded. The First Line of Defense: Overload Clutches In high-speed automation and heavy industrial machinery, a "jam" is not a matter of if , but when . Whether it is a cardboard box getting stuck in a packaging machine or a tool crashing in a CNC lathe, the resulting torque spike can destroy gearboxes, twist shafts, and burn out expensive servo motors in milliseconds. A torque limiter (or overload clutch) is the mechanical fuse of the drive system. While electronic monitoring (current limiting) is common, it is often too slow to prevent physical damage from the massive kinetic energy stored in the system inertia. A mechanical torque limiter provides a physical disconnect that operates in a fraction of a second. Search for Torque Limiters & Safety Couplings Advertisement Why Choose ...
Post a Comment
Read more about this Mechanical Design Article »

Cam Design Essentials: Kinematics, Pressure Angles, and CNC

Mechanical cams remain the "heart of automation," providing precise timing and motion control in high-speed machinery. Understanding the geometry and dynamics of these systems is essential for modern machine design. Advertisement Classes of Cams Cams may, in general, be divided into two classes: uniform motion cams and accelerated motion cams. The uniform motion cam moves the follower at the same rate of speed from the beginning to the end of the stroke. However, as the movement starts from zero to full speed instantly and stops in the same abrupt way, there is a distinct shock at the beginning and end of the stroke if the movement is at all rapid. In machinery working at a high rate of speed, therefore, it is important that cams are so constructed that sudden shocks are avoided when starting the motion or when reversing the direction of motion of the follower. The uniformly accelerated motion cam is suitable for moderate speeds, but it ha...
2 comments
Read more about this Mechanical Design Article »