Bulb Finger Joints are useful and attractive co-planer joints for connecting different sheet materials which are very easy to produce with machines such as CNC routers, Water Jets & Lasers. A great benefit of these joints is the strength along the plane of the joint without having to glue/ weld.
This Instructable shows the simple geometry behind this joint and explains how to draft this & how you can adapt its form to allow for greater control of the technique and hence the overall design.
I'm explaining this in terms of drafting it with programs that can export to the manufacturing tools capable of fabricating these components, though the form can be achieved with a basic compass set.
Thank You TechShop Detroit for helping me with this design :) www.techshop.ws
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Step 1: Basic Geometry Overview
The bulbs are created by a vector slalom between regular circles that are tangent to each other.
Specifically, at the diagonal tangent of eachother about a stright line (spine) being slalomed.
This means that if you draft a circle and draw a perfect X through its center to the circumference, the intersection of this line with the circumference should meet along the 'spine' of the connection, joining with the same point of other circles.
This way the circles are stringed together by these diagonal tangents alternating along this spine. Once the chain is complete all you need to do is delete the shorter segments of each circle or create a new layer and trace as you want using this as a framework.
Step 2: Creating the Boundries for the Bulb Chain
Here i am showing the shape i want the Bulb Joint Chain to link within. Here I'm creating a long eye type shape. The line dividing the form is the 'spine' which the chain will fall along. The form does not have to be symmetrical across this line here it is.
If your using a CAD program, once you have established this form you can lock the layer and start a new one using this as guidelines.
Step 3: Layout of Circles
1-Starting at one end of the spine, scale a circle so that the X intersects the spine as well as being tangent to the outer perimeter while packing it into the corner as small as you want to start the scheme.
2-The next circle fits in on the alternate side of the spine at its intersection with the x intersection furthest intersection from the starting end on the spine.
3-The third circle starts the same side as the first circle but connecting x's with the second cricle on the alternate side of the spine.
Continue in such a way until you have fully packed the form; This way the X's create an alternating latticework either side of said spine with a chain of circles tangent along the spine as well as the bounding guidelines.
Step 4: Remove / Use Guidelines
You can either produce the form by deleting the parts of the framework that are not the bulb lobes or trace the form on a new layer. At this stage, both techniques provide the space to edit the shape to adhere to or alter the form. The shape can be as irregular & rough as you like as either side of the this vector - when included as part of the perimeter of a plane - will mate precisely with each other.
Step 5: Curving (Elastic) Spines
One handy technique i found in Illustrator (or similar) , is that you can turn the pattern you created - with a stright spine- into a 'pattern brush' that you can lay along any curve and 'apply' the brush treatment to bend the spine to match the curve. Once you have produced the curve your after and applied the brush, you can 'expand appearance' which will replace the original vector you laid the pattern brush along into the 'expanded' form a.k.a an exportable vector of your Bulb Slot Chain.
Step 6: Creating Curved Spines
There is no reason the Spine has to be straight though there is an extra step in that you not only have to scale each circle but also rotate them; The x's from the circles need to connect with each-other intersecting and alternating at the spine. The best way to do this is connect the circle with the previous circle then use the x connection as a fulcrum to rotate untill the other part of the x touches the spine further on. The next stage is to scale the circle-x group from the fulcrum. At this point some iterative shimmying is probably easiest until a tolerable placement and scale is found rotating and scaling several times until satisfied.
This process is very good if you asolutly know what how you want the spine to curve but does not provide much flexibility.
Step 7: Other & Recursive Forms.
There is nothing stopping you from using a Bulb Joint Chain as a Spine for a more fine-grain Bulb Joint Chain, other than sense and time parameters.
I've included this slide to demonstrate a different binding shape for laying out the framework.