How to Design a Hoeken’s Straight-Line Linkage in Excel (with VBA Simulator) Figure 1: Geometry of the Hoeken’s straight-line linkage and resulting coupler-point trajectory. The lower portion of the curve approximates straight-line motion over ~180° of crank rotation. The Hoeken’s Linkage is a mechanical engineer's favorite magic trick. It is a four-bar mechanism that converts simple rotational input into a near-perfect straight-line output. Unlike the Watt Linkage (which traces a figure-8), the Hoeken’s Linkage creates a "tear-drop" shape with a long, flat bottom (see Figure 1). This makes it the standard choice for walking robots and intermittent linear actuators. But how do you find the link lengths? If you guess, you get a wobble. This guide provides practical "Golden Ratios" and an Excel VBA tool to simulate the motion path. 1. The Geometry: Practical Design Ratios To achieve a usable straight line, link lengths m...
Normally we can find a lot of ball joints (rod ends) with pull rods on almost every machine. They are used to transmit power from a lever to another link in cams or pneumatic driven mechanisms. It is the part of the system that allows us to adjust the length to compensate for imperfections in the manufacturing of machine parts.
For example, we may require high accuracy of a mechanism at one position, but we cannot achieve it with a fixed-length rod; therefore, the use of an adjusting rod is required.
The Standard Approach: Turnbuckle Style
This standard adjusting rod consists of a right-handed (RH) ball joint at one side and a left-handed (LH) ball joint at the other side. This is because we need to adjust the distance between the centers of both ball joints by turning the pull rod.
When turning the rod, the screw threads will increase or decrease the distance depending on the turning direction. (If we used right-handed ball joints at both sides, turning the rod would simply shift the rod left or right without changing the total length!).
Normally, coarse threaded ball joints are used because they are standard. However, this creates a limitation on accuracy.
The Calculation:
Let's look at the example in the picture above using two M8 ball joints (LH & RH threads).
The standard pitch of an M8 screw thread is 1.25 mm.
Because one side moves out 1.25mm and the other side moves out 1.25mm simultaneously:
1 Revolution = 2 x 1.25 = 2.5 mm change.
This is often too coarse for precision machinery. How can we get more accuracy? Shall we change to M6 (1mm pitch)? Or use special fine threads?
The Design Trick: Differential Screw Principle
We can do anything, but the trick in this post is to use the Differential Screw principle. We put an additional M10 coarse thread in between the two sections and separate the pull rod into two pieces.
How it works:
- Thread A: M8 Coarse (Pitch = 1.25 mm)
- Thread B: M10 Coarse (Pitch = 1.5 mm)
Now, when we turn "pull rod 1" by 1 revolution:
- It pulls the M8 ball joint IN by 1.25 mm.
- At the same time, it pushes "pull rod 2" OUT in the same direction by 1.5 mm.
Therefore, the total change in the length of the adjusting rod is the difference between the pitches:
1.5 mm - 1.25 mm = 0.25 mm!
(Of course, there should be a jam nut to lock the final position, which is not present in the simplified picture).
Conclusion
With this simple technique, we can achieve much higher accuracy for length adjustment using standard coarse threads. Ten turns of this new rod change the length by the same amount as just 1 turn of a normal adjusting rod.
I hope this trick is useful for your mechanical design projects!
Comments