What Rubber is Best for Laser Cut McKibbens PAMs?

There are silicone specific adhesives, as silicone does not adhere well to any other material. Appropriately, there are rubber adhesives for genuine rubber as well. The method you describe is going to severely test the adhesion of the material, as it places the most stress along the weakest points in the system.

Have you considered using surgical rubber tubing as the foundation of the system build? I've used this tubing for elastic properties as in a slingshot, but also in an inflation mode (without the sleeve). It works well in the latter instance, as long as the system is not exposed at length to sunshine or chemical fumes of any sort to degrade the silicone. The inflation mode was with water and the resulting rupture was more amusing than dangerous.

A "finger-trap" sleeve as reference in the documentation I've found would help with the longevity of the system.

McMaster-Carr carries such tubing from inside diameters of 1/16" to 1" and 2 mm to 8 mm.

Response to comments: If joining surfaces is preferred to adhesives, your method of heating the surfaces will determine the strength and is likely to be stronger if the process is done properly.

The information I've seen in this respect use a heated blade. It's typically mounted in a jig which directs the "tubular" form of material in such a way as to contact the heated blade simultaneously, while the jig compresses the shape at the contact point.

It's critical to have sufficient energy imparted to the blade to continually compensate for the heat removed by the melting process and to have a well-regulated speed over the blade.

I've laser cut silicone sheet and the mechanical characteristics of the sheet were not changed, although the edges were "cleaner" as a result. I've not cut latex rubber but a quick search indicates that it is not a problem. Cutting any product containing polyvinyl chloride compounds is dangerous, but latex rubber should not have such a compound.

Consider to edit "patters" to "patterns" as I didn't understand at first the reference, not having read all the papers found for this item you desire to construct.

Another option you may wish to consider is to create your specific shapes using 3D printed molds and casting the latex rubber within. This would provide for your custom modifications as well as reduce/eliminate adhesives and bonding complications. The realm of possibilities with a 3D printed mold is exhaustive.

I use OpenSCAD for creating 3D models, which is useful for repetitive mathematical designs, although many of the CAD programs such as Fusion 360 permit parametric modeling as well.

Due to the flexibility of the rubber, you'd be able to create molds that might otherwise not release the part. Alternative methods would include using a water soluble support filament such as PVA which washes away with water, for more complex designs. Vacuum processing during the mold pour may be necessary for more intricate models, but I'm getting ahead of myself.

Even though marked as accepted, additional thought of the matter also suggests that one may want to consider 3D printed versions using TPU filament. It's very "stretchy" and would allow for infinitely complex structures. I've not tested porosity but the substance melts during the printing process and does not delaminate when stretched.