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 »
Disclosure: As an Amazon Associate, I earn from qualifying purchases.

3-Position Synthesis with Inversion Method (Introduction)

In our previous tutorials, such as [3-Position Motion Generation Synthesis with Alternate Moving Pivots], we used a "standard" synthesis approach. We defined the moving coupler first, and the geometric construction dictated where the ground pivots (O2 and O4) had to be.

But what if you don't have that freedom?

Advertisement

In real-world machine design, you often have a pre-existing frame or base. You cannot drill holes just anywhere; the ground pivots must be located at specific, available points. In this scenario, the standard method fails because it gives you valid kinematic solutions that might require mounting a pivot in thin air or inside a motor.

The Solution: Kinematic Inversion

To solve this, we use the Inversion Method.

The Core Concept

Instead of looking at the mechanism from the perspective of a stationary ground and a moving coupler, we invert our perspective.

We pretend the Coupler is stationary and the Ground is moving.

By fixing the coupler positions (A1B1, A2B2, A3B3) on top of each other, we can rotate the ground pivots backwards relative to the coupler. This allows us to geometrically find the required length of the input and output links that connect our specific ground points to the moving coupler.

Why use the Inversion Method?

  • Fixed Ground Constraints: Essential when you must attach links to specific pre-drilled holes or mounting pads on a machine frame.
  • Compact Design: Helps in designing mechanisms that must fit within a tight housing where pivot locations are limited.
  • Complex Motion: Often easier to visualize relative motion between the end-effector and the base.
Advertisement

What to Expect in Part 2

In the next post, we will walk through the step-by-step CAD procedure:

  1. Defining the 3 desired positions of the coupler.
  2. Defining the Fixed Pivot Locations (O2 and O4) first.
  3. Using CAD transformations to "invert" the ground points.
  4. Finding the center of the circle defined by these inverted points to determine link lengths.

This method is a powerful tool in the arsenal of any Mechanism Design Engineer.

Recommended Reading

Kinematic Synthesis of Linkages
(Hartenberg & Denavit)

Check Availability
Design of Machinery
(Robert L. Norton)

Check Availability
Labels:

Comments

Post a Comment

Popular posts from this blog

Flywheel Construction and Design: A Guide to Energy Storage Wheels

A flywheel is a mechanical device with a significant moment of inertia used as a kinetic energy storage reservoir. Flywheels are designed to resist changes in rotational speed, helping to steady a shaft's rotation when a fluctuating torque is applied (as seen in reciprocating engines) or when the load itself is intermittent (such as in piston pumps or punching presses). Advertisement Beyond smoothing rotation, flywheels are increasingly used to produce high-power pulses for industrial experiments. In these cases, drawing the required instantaneous power from an electrical network would create unacceptable spikes. Instead, a small motor slowly accelerates the flywheel between pulses, storing energy to be released in a single high-torque event. Figure 1: Modern flywheels are sophisticated energy storage systems for steadying rotation and delivering power pulses. 1. Classification: Balance Wheels vs. Flywheel Pulleys Flywheels are gene...
Post a Comment
Read more about this Mechanical Design Article »

Dowel Pins & Locating Pins: The Basics of Fixture Design

Dowel pins are precision cylindrical pins used for accurate part alignment in assemblies. They control position, not clamping force. This guide explains tolerances, fits, sizing rules, and design best practices. 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-wea...
Post a Comment
Read more about this Mechanical Design Article »

Roberts straight-line mechanism

Figure 1: A modern linear ball slide (like this THK model) is the contemporary solution for precise straight-line motion. Many modern engineering applications require components to move in a precise linear fashion, known as " straight-line motion ". Today, we take this for granted. We can simply purchase an off-the-shelf Linear Motion Guide that moves a device accurately along a rail with low friction. The Historical Challenge: Making a Straight Line However, in the late 17th and early 18th centuries—before the development of high-precision milling machines—it was extremely difficult to manufacture long, perfectly flat surfaces. Creating a sliding joint without significant backlash was nearly impossible. During that era, engineers had to rely on Linkages . Much thought was given to the problem of attaining a straight-line motion using only revolute (hinge) connections, which were much easier to manufacture. The most famous early result was...
Post a Comment
Read more about this Mechanical Design Article »