When woodworking plans call for cutting curves in thick stock, the band saw is usually the instrument of choice. Band saws are simply adjustable to accommodate most stock thicknesses, and the blade remains straight throughout the cut (a challenge when cutting thick stock with some other tools). However, if you don't have access to a band saw or need to perform an interior cut (on the inside of a piece of stock rather than cutting from the edge), you have a few options. Each has perks and disadvantages.
Jigsaw
A jigsaw is a handheld version of a band saw for many amateur woodworkers and DIYers (or, more precisely, a scroll saw, which is another option for curved interior cut-outs). Jigsaws can cut a wide range of stock thicknesses, including up to five inches. To make interior cuts, drill a starting hole into the cut-off area using a 3/8 or 1/2-inch bit. The jigsaw blade is then inserted into the hole to begin the cut. The disadvantage of using a jigsaw to cut thick stock is that longer stock requires a longer blade, and a longer blade is more likely to bend during the cut, resulting in a cut edge that may not be as vertical or as clean as you'd want. Using a larger blade reduces flexing, but larger blades do not revolve as securely as smaller blades, therefore there is an inherent trade-off. To ensure that the blade clears the sawdust during the cut, the blade should be at least one inch longer than the thickness of the stock.
Coping Saw
Coping saws are specialized handsaws used to cut very tight curves in thinner stock, such as trim moulding. However, they will suffice for outside (from the edge) cuts on relatively thick stock, say up to two or three inches thick. Coping saws provide precise control, allowing you to chip away at your own pace. Coping saws have three disadvantages. First, they have very thin, sensitive blades that bend and break quickly, so you must be extremely careful to keep your line straight at all times. Second, the blade length is small, resulting in a short cutting stroke and a lot of work for you. Third, the cutting depth is restricted to the depth of the saw's frame (or the throat distance), and the frame frequently gets in the way while cutting parallel to the edge of the stock. This constraint can be mitigated considerably by performing relief cuts to remove superfluous material as the curve develops.
Reciprocating Saw
Reciprocating saws are intended for demolition rather than carpentry, but they will handle rough cuts in heavy stock such as landscape timbers or thick joists. To avoid the jarring bouncing effect associated with these monstrous tools, keep the blade speed up but advance the tool gently. Just be careful not to overheat the blade and burn the wood. Use a wood blade with a thin profile to create sharper curves.
Router
A router makes very clean cuts and can handle stock of varied thicknesses; the thickness is determined by the bit length and your comfort level. Working with lengthy bits necessitates extra caution and safety precautions since long bits can flex and chatter if pushed too hard. In most cases, a rough cut with a jigsaw removes the majority of the waste, followed by a router cut to remove the last 1/16 inch or so. Hogging out a large amount of material with a router is difficult on both the bit and the tool. Create a blueprint for the router to follow for the final cleanup for the cleanest cut.
