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...
In advanced Mechanism Design, we often face the challenge of moving a rigid body from one specific position to another. This process is known as Motion Generation Synthesis.
While sophisticated solver software exists, you can perform this synthesis geometrically using the Constraint-Based Sketcher found in any modern CAD package like Unigraphics NX (Siemens NX), SolidWorks, or CATIA.
The Goal: Moving a Line in a Plane
Assume we need to design a 4-bar linkage that moves a coupler link from position AB to position A'B'.
Step-by-Step Geometric Synthesis
1. Define the Positions:
Draw the link AB (Start Position) and A'B' (End Position) in the NX Sketcher.
2. Locate the First Pivot (O2):
Draw a construction line connecting point A to A'. Create a Perpendicular Bisector of line AA'.
Theory: Any point located on this bisector is equidistant from A and A', meaning it can serve as a fixed pivot point.
3. Select Pivot O2:
Select any convenient point on the bisector to be the fixed ground pivot O2.
(Example: Length O2A = 500 mm). Draw line O2A to represent Link 1.
4. Locate the Second Pivot (O4):
Repeat the process for points B and B'. Draw a line from B to B' and create its perpendicular bisector.
5. Select Pivot O4:
Choose a point on this bisector to be fixed pivot O4.
(Example: We selected a 60° angle). Draw line O4B to represent Link 2.
Constructing the Kinematic Chain
Now we build the full linkage to test the motion:
- Draw line O2M equal in length to O2A.
- Draw line O4N equal in length to O4B.
- Draw the coupler line MN equal in length to AB.
- Apply geometric constraints to ensure the chain stays connected.
Validation via "Animate Dimension"
To verify the synthesis, we use the Animate Dimension tool.
Set an angular dimension between the ground and the input link. Configure the animation range (e.g., 0 to 60 degrees) and step count (150 steps for smoothness).
Watch the Kinematic Synthesis Result:
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