How to set the transform origin to a specific point on the element?

To make the transform-origin point relative to the element, you need to use transform-box: fill-box;.

Chrome doesn't support that property yet (CSS transform-box - Chrome Platform Status), but luckily (yet wrongfully) Chrome sets the transform-origin relative to the element if you use percentages instead of pixels (https://css-tricks.com/transforms-on-svg-elements/).

So, to make something that works on most *) modern browsers, use transform-box: fill-box; and transform-origin: xx% yy%;

.hammer-icon {
    transform-origin: 15% 80%;
    transform-box: fill-box;
    ...
}

https://jsfiddle.net/L1790vzo/8

*) IE/Edge doesn't support CSS transforms on SVG elements at all.
*) Proper support in Chrome v64 and Opera v51