If the base of a circular saw is not sturdy enough, the weight of the saw can cause the end of the motor opposite the blade to dip while in use. A cut that was supposed to be a square edge suddenly produces a bevel. And, the shift in blade angle from the dip of the motor can cause the saw to wander off of the line you set.
Just about all saws available for less than $100 US have steel bases stamped from relatively thin metal. While in a store, raise the blade as if for a more shallow cut, lock the adjustment nut, and press on the base with your thumb as shown in the photo. On many saws you will see the base deflect. The base is too weak. But, you can strengthen it.
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Step 1: Add Additional Support
I opened the motor case on my saw and found a place where I could drill a hole for a 1/4 inch x 20 thd. cap screw without interfering in any way with the motor. (See the wing nut on the screw end in the photo where the cap screw comes out of the motor just to the right of the venting slots.) I held it in place with a locking nut on the outside of the motor. The possibilities for doing this will vary with the exact configuration of your saw.
The steel piece with the adjustment slot is from 1/8 x 1 inch strap iron about 6 5/8 inches long. The slot was cut with a friend's oxy-acetylene cutting torch. (Grind away any bumps left by molten metal.) The slot needs to be long enough to cover the full range of adjustment possible on your saw from the lowest motor position to the highest, from a fully vertical blade setting to a full 45 degree bevel, and with any combination of both.
The slot could also be cut with a hacksaw (after drilling a couple of holes next to one another to make an opening for inserting the blade and then re-attaching the blade in the hacksaw frame). A cutting wheel on an angle head grinder could also be used, although it is easy to wander off of the desired line with an angle head grinder.
Step 2: Fastening the Hinge to the Saw Base
Because I had access to my friend's oxy-acetylene welder, I brazed a scrap hinge to the base of the saw. Bevel head screws with countersinking for the heads would also work fine. I would use self-locking nuts. The slotted support bar needs to swing side to side on an axis. It is attached to the hinge with a 1/4 inch bolt and a self-locking nut.
To use the saw with the additional support in place--
When making any adjustment in the bevel or depth of cut on the blade, first loosen the wing nut on the slotted bar. Then loosen either the saw's bevel adjustment or the depth of exposed blade adjustment. Position the saw base relative to the blade. Lock down the factory provided adjustment you are changing. Then lock down the wing nut on the additional support bar.
This extra support bar allows you to do accurate work with an inexpensive saw, even though it has a weak or somewhat flimsy base.