Finding the Missing Links

May 25, 2006
Here's how to design mechanical linkages without solving a single trig equation.

Matthew Sawhill
Mechanical Engineer
Townsend Engineering
Des Moines, Iowa

The tube-handling mechanism looks like this when finished. But for starters, all you know is the loading and chucking position for the tube, and an allowable volume. The model and sketches are made in AutoDesk Inventor.

The final linkage

A little more geometry makes the link lines look real.

Modern CAD systems include powerful sketching tools. One application that gets little publicity helps design mechanical linkages using the sketcher's para-metric features. An example shows how to design a four-bar linkage for a tube-processing machine without solving a single trigonometric calculation or even using a calculator.

In the mechanism, tubes enter the machine to a "waiting position" where a linkage moves them to a "loading position". They are aligned before insertion into a chuck.

The task is to design the linkage that moves tubes from the waiting to the loading position. To make the design more realistic and challenging, it reuses a standard air cylinder left over from a previous project.

Step 1 begins with a CAD program, AutoDesk Inventor in this case, to create a simple sketch that defines the tube's two positions. A construction line joins the two positions and shows an approximate path of the tube as it travels from one position to the other.

Sketch a basic four-bar linkage to represents base A, two upright links, B and C, and the link representing the gripper arm D. A triangle represents link D. The vertices of the triangle represent the connections to links B and C, and the position of the gripper in one of its operating positions.

The exact size or proportions of the linkage are not critical. The CAD software will size components as the design progresses. The important thing is to create the design's geometric building blocks.

It's a good idea to turn off automatic constraining features in the CAD software while designing the linkage. This lets you control the sketch's constraints. Extra constraints can unintentionally sneak into the design with frustrating consequences as it continues.

Step 2 builds "intelligence" into the sketch by constraining the geometry. For instance, links A, B, C, and D must maintain the same shape throughout the travel of the linkage. In this design, the CAD system's Equal Constraint feature (in Inventor) ensures each link maintains an equal length in both positions. For instance, lines C and C' are constrained to be of equal length, because they represent the same physical link.

Step 3 experiments with different designs. In this step, the sizes of linkage components are unconstrained, so the geometry is free to float in the sketch. This lets users click and drag the linkage to visually experiment with different configurations before committing to final dimensions.

The air cylinder that must be part of the design has a retracted length of 6 in. and an extended length of 7.5 in. For simplicity, the cylinder will be mounted to linkage joint pins A-B and C-D. The cylinder is represented by simply dimensioning the distance between pins in both linkage positions.

Step 4 begins with a linkage that meets requirements. But there is still freedom to tailor the design to the installation. In this step, the design is placed in the imaginary tube-processing machine and the remaining degrees of freedom in the design will be used to ensure a good fit in the actual machine cabinet.

The final linkage shows the geometry for just that. In this case, the final form was selected to avoid interference with other machine parts, and to position the base of the linkage for convenient mounting in the machine frame.

Throughout the design process, the power of the sketching tools made it easy to visualize and adjust the linkage for best performance. Though the example is relatively simple, the same concepts can be applied to more complex linkages.

Step 1 identifies the location of the tubes and sketches out an arbitrary four-bar linkage.

Identifying joints in the linkage lets users pull it from one position to the other.

The 6-in. cylinder has a 1.5-in. stroke, so the 6 and 7.5-in. positions can be defined. The software adjusts the lengths of the other linkages.

Sketching the 2D boundary of the box allows adjusting other link lengths.

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