Posted November 17, 2016
How to Design a Turner's Cube
A turner’s cube is a classic machinist’s exercise that involves constructing multiple cubes inside of one another. This effect is achieved by boring holes of decreasing size and increasing depth to reveal each cube as the layers of material are stripped away.
Start your turner’s cube by deciding on the size of your largest cube and the number of total cubes you want it to have. Today, I’ll be making an outside cube with edges of 1.2” and 2 inner cubes, to make a 3-layer turner’s cube. I’ll be sketching the design steps out in SolidWorks, but feel free to use a pen and paper, or your preferred CAD program, to make these calculations instead.
First, to determine the width of each inner cube, we must calculate how much smaller each cube will be than the cube in which it nests. To calculate an even interval, divide the total width of the cube by the number of layers; in this case, 1.2"/3 layers = 0.4" per layer. This number corresponds to how much the width of each cube will shrink from layer to layer. In the example, the outermost cube will be 1.2" wide, the middle cube will be 0.4" smaller (0.8" total width), and the innermost cube will be 0.4" smaller (0.4" total width).
Now you have to calculate the diameter of each hole you make. The diameter will have to be smaller than the corner-to-corner distance of the cube it is “revealing”. For instance, our small cube is 0.4”. Using the Pythagorean Theorem, a2+b2=c2, we know that the cube’s corner-to-corner distance is about 0.57”. Anything smaller than the cube’s face won’t reveal its edges, so your hole will have to be between 0.4” and 0.57” across. I’ll be using a hole with a radius of 0.5”.
For your medium cube, your hole will have to be between 0.8” and 1.13” in diameter. This hole is 1.0” across, but feel free to adjust yours to the size you find most visually appealing.
If you want to drill a hole through the small cube, the diameter will simply have to be smaller than the cube’s width, 0.4”. For example, this hole has a diameter of 0.16”.
Finally, we calculate how deep each hole in the cube will go. We do this by subtracting each cube’s width from the largest cube’s width, and dividing that by 2. So, the small cube’s hole will be (1.2-0.4)/2, or 0.4” deep, and the medium cube’s hole will be (1.2-0.8)/2, or 0.2” deep. The smallest bore will go all the way through the piece. Below is a completed a sketch of our turner’s cube.
Now that we’ve determined the dimensions of our turner’s cube, it’s time to construct a 3D model of it in SolidWorks. First, create a new part, then draw and dimension a 1.2” x 1.2” square centered on the origin. Go to the “Features” tab in the upper lefthand corner and select “Extruded Boss/Base”. You should be able to use this feature to raise your square to a height of 1.2”, making your base cube.
Now, choose a face of your cube and sketch a circle with a diameter of 1.0” (a radius of 0.5”) starting at the origin. After you’ve created the circle and used the “Smart Dimension” tool to set the radius to 0.5”, move back to the “Features” tab and select “Extruded Cut”. In the lefthand menu, make sure that “Blind” is selected in the “Direction” section, and set the depth to 0.2”. Select the green check mark in the upper right hand corner of your screen to confirm the cut.
Repeat this step with a 0.25” diameter circle with a depth of 0.4”.
Now we’re going to make the center hole, which we will do with the “Hole Wizard” tool in the “Features” tab. Select the “Hole” option in the upper righthand corner of the grid, set the “Size” to #20, or 0.161”, and set the “End Condition” to “Through All”. Move to the “Positions” tab at the top of the Hole Specifications menu, select the face you plan to drill the hole through, and center the hole at the origin. Click the green checkmark to confirm.
You have now completed one face of your turner’s cube!
There are many different ways to copy this face to the other 5 sides of your cube, most of them variations on reflection and rotation of existing features. We are going to replicate your cube’s featured face by creating 2 axes and revolving these features in a circle around them.
To make your first axis, go up to “Reference Geometry” and select “Axis” from the dropdown menu. Select one of the cylindrical faces of your extruded cuts to center the axis, and confirm your changes.
To create your second axis, go to the “Sketch” tab, select “Point”, and choose a face perpendicular to the face your features are currently on. Create a point at the exact center of the face. Return to the “Features” tab, select “Reference Geometry”, and select “Axis” from the dropdown menu again. This time, select the point you just drew, and the face of the cube parallel to the one you drew the midpoint on. Click the green checkmark to confirm.
Now, click on the arrow below “Linear Pattern” and select “Circular Pattern” instead. Select your second axis, set the “Angle of Rotation” to 90°, and set the “Number of Instances” to 4. Then, select the two extruded cuts and the hole you made in your cube’s primary face. Confirming this should move the holes and extruded cuts to 3 more of your cube’s faces.
To move your features to your cube’s remaining 2 faces, select “Circular Pattern” again, and select your first axis. Make sure the “Angle of Rotation” is 90°, then set the “Number of Instances” to 2. If the circular pattern you just made isn’t automatically selected, select it from the dropdown tree in the upper left hand corner of your screen, and confirm your changes.
Congratulations! Your turner’s cube is now complete.
To order your turner’s cube, save your part, then open the Plethora add-in by clicking on the small “P” logo on the righthand side of your screen. Analyze your part for manufacturability and place your order. A turner's cube of this size will come in under $250, so if you're looking for a free part to spend your credit on, this is an option! We will mill your turner’s cube and ship it to you on or before the date you select in the ordering process.
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