Handles are a very important part of a mug; if it's not comfortable, you will never use it, defeating the whole purpose. I have spent years researching handles and also exploring other handles people have come up with. Figuring out what works and what may just work as a decorative piece.
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What you will not find here:
1) "Curly q's" at the bottom of the mug, they often don't come out nice enough to justify. They are supposed to be cute or fancy, but will often come out kind of visually lumpy and throw off where the pinky will land on the mug, making it just in the way. It also gives one more breaking point on the handle.
2) Oversized thick handles meant for the hulk, while yes, this does make the mug more sturdy in the handle area and less likely to break in the handle area, I have seen them take off whole sides of mugs because the weight is just not balanced. Place it down wrong and there goes the whole side of the mug. A mug is often 1/4" thick, those thick handles are often 1-2 inches thick, the weight distribution can cause issues for the mug body, but the handle will be ok. It is also very difficult to hold often causing slipping, or just hard to grip altogether, and it will add a lot of weight to the mug both visually and physically. I often find myself bypassing the handle altogether if the handle is super thick.
3) the super thin whimsical handle that reaches out twice the width of the mug, this is just asking to break, one wrong placement or movement and they will break off in an instant, also when the mug is full, it may not have sufficient strength or balance to hold up the mug without breaking. I often see people 'clawing' the mug just in order to hold it.
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Thumb-rests, I always see about putting a thumb rest on, it's on about 99% of my mugs. What you will not see me do is putting it on the "correct way'' other potters often say, I use thumb rests as leverage for counterbalance, not something to push against. I want you to enjoy drinking coffee, not fighting it off. The only place where that may be applicable is on large mugs used for chugging when it's lifted over your head.
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With that said, I have explored making dozens of styles over the years, and I still make a number of them just for variety, but currently, I usually only make 4 types these days.
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The one I make most is the "two-three finger hold", or the 'ear handle'. Often put on average-sized mugs, the thumb goes on the thumb rest, 2-3 fingers go inside the handle, and then either the ring or pinky finger on the outside bottom for balance. a great versatile handle that can go on many forms. Very comfortable and natural feeling, often great for "cupping'' mugs with the second hand.
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I do make a variety of one-finger mugs, but not often, usually reserved for espresso mugs or small mugs, often smaller than 6 oz. Some are meant for gripping the handle, some are meant to put the finger through the handle with the rest of the hand around the mug, just acting as an extra grip.
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Gripping mugs usually will have concave points and ridges to help grip and rest fingers in. I make this variety mostly for my straw mugs, or sip mugs. Other mugs such as tea mugs and yunomi style I would often leave a large indented foot for grip, as well as a few finger indents for extra grip as well.
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Full-handed handles are something I'm currently working on. I don't want it thick where it feels hard to grip, but not thin enough where you feel like it's going to break. I am still searching for the ideal balance in this now that I am going back to making large mugs again. I often "square" them off, so the handle doesn't stick out like crazy, causing the balance to be thrown off and risking it bumping into things and breaking. I am liking this shape and style but I am still working on how to make it more comfortable and more sturdy without throwing off the balance and comfort. The "ear" shape handles seen with the 2-finger mugs will not work for this. Often, the pinky will be squished at the bottom point, making it awkward, not knowing if you want it on the inside or out. Or, the top of the ear would be so far out that the leverage will be thrown off, or it could easily be bumped and broken, so on my larger pieces, you will often see my "bracket' shaped full-handed style, but it is still something I am not 100% satisfied with just yet.
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I go for a medium thickness in my handles. Too thick will cause wobbliness and struggle, too thin can increase breakage, and feel too dainty and may cause slipping if the mug gets too heavy with coffee in it. A medium-sized handle is great in between offering balance and comfort, but needs more caution than the thick beast of a handle. If you are clumsy, this may not be the handle for you. But after a decade of use I have not broken any, and my child has been using them for years since he was two years old, and has not broken any either.
**A quick note on Mug Thickness** I aim for 1/4" thick, offering strength and lightness. If a mug is too light, it feels way too fragile to use; lightness is not always good or sturdy, too thick and it would feel too heavy to use, especially when full, and may be better off as a paper weight. I sometimes leave mugs thicker if I intend to carve them.