The Solution: When you need to increase machine throughput without increasing acceleration forces, the answer is almost always overlapping motion.
However, overlapping mechanisms in tight spaces introduces a severe risk of catastrophic mechanical collisions. To validate this 25% speed increase safely, I didn't use expensive 3D motion analysis software. Instead, I used Microsoft Excel and VBA to build a custom 2D kinematic simulator. Here is how that mathematical model was built, and how that exact machine is still running in production over two decades later.
(Note: This image is an AI-generated illustration for conceptual purposes and does not depict the actual 2005 production machine.)
Table of Contents
1. The Speed Limit in Machine Design
When plant managers ask engineers to increase machine throughput, the instinct is straightforward: turn up the VFD frequency or change the gear ratio. In practice, this brute-force approach quickly hits a brick wall.
Because Force equals Mass times Acceleration (F = ma), higher speeds drastically increase acceleration. This results in exponentially higher inertial forces, severe machine vibration, premature bearing fatigue, and product damage. For machines handling delicate payloads like glass, excessive acceleration is the ultimate limiting factor.
2. Sequential vs. Overlapping Motion
To safely increase throughput, you must eliminate idle time in the machine's 360-degree master cycle.
| Motion Strategy | Machine Cycle Example | Throughput & Risk Profile |
|---|---|---|
| Sequential Motion | 1. Turret indexes to position. 2. Turret comes to a complete stop. 3. Gripper moves down. 4. Part is transferred. |
Low Risk / Low Speed. Extremely safe, no chance of collision, but highly inefficient due to accumulated idle time. |
| Overlapping Motion | 1. Turret approaches final index position. 2. Simultaneously, gripper begins downward stroke. 3. Gripper enters turret slot perfectly as turret stops. |
High Speed / High Risk. Maximizes throughput without increasing acceleration, but timing errors result in mechanical crashes. |
Implementing overlapping motion meant the gripper would be entering the turret slot while the turret was still rotating. Even a 3-degree cam timing error would cause the steel gripper to violently strike the aluminum turret. I needed absolute mathematical certainty.
3. Building the Kinematic Simulator in Excel
Today, engineers use advanced CAD motion software to verify clearances. In 2005, I relied on Microsoft Excel and a trusty VBA programming guide. The spreadsheet was designed to calculate the position of every mechanism based on the machine’s master timing diagram.
By mapping the multi-axis motion of the turret and the gripper across the full 360-degree machine cycle, the spreadsheet utilized standard trigonometric functions to produce the exact X and Y coordinates of each moving part at any given degree of rotation. This provided the rigid mathematical foundation of the simulation.
4. Visualizing the Clearance with VBA (Video Demo)
Numbers in a spreadsheet are not enough to confidently verify a dynamic mechanical clearance. To truly visualize the overlapping motion, I wrote a Visual Basic for Applications (VBA) macro that stepped through the machine cycle one degree at a time.
For each loop of the macro, variables such as the cam angle, turret rotation, and gripper elevation were updated. Excel recalculated the geometry instantly, and the resulting coordinates were plotted on a standard 2D XY scatter chart. Watch the video below to see the actual macro animation in action:
As the macro ran, the chart animated the machine motion in real-time. I could watch the gripper safely enter the turret slot while the turret was still rotating, confirming visually that the mechanisms cleared each other throughout the entire 360-degree cycle.
5. From Spreadsheet to 21 Years of Production
Once the Excel simulation verified the timing, we translated that exact motion data into the final machine design, defining the cam timing profiles, motion synchronization, and safe mechanical limits.
The upgraded system successfully achieved the target 1,500 UPH (a 25% throughput increase) without introducing a single damaging acceleration spike to the fragile glass payload.
Sometimes the most powerful engineering tools are not expensive software platforms. They are a solid understanding of machine kinematics, strong engineering fundamentals (like those found in Machinery's Handbook), and the creativity to build your own tools.
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This article is written by a senior engineering leader with over 25 years of experience in industrial automation, process optimization, and mechanical design.
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