At the beginning my biggest problem with quadrupeds was that I saw too many things going on - too many limbs in motion, too many lines to follow, too many masses:
When doing gesture drawing of humans the most important line is usually the backbone, and all other lines follow logically from it. Sometimes it is obvious in quadrupeds too:
But I look on purpose for weird poses where it is hard to figure out which lines are the most important for the overall shapes. Giraffes have unusually long legs, the neck is a unique feature which changes a lot the visual balance of their body, and on top of that their movements are very constrained. So trying to make giraffes look agile and not stiff is an interesting exercise.
The little figures on the right are a possible way to sketch quadruped poses considering only a few main lines and masses. I did a lot of them too and it turns out they are also a good exercise in synthesis, to train oneself to remember well the proportions and two or three key features of a species. The can be useful to study features at any level, for example to study small differences between species which look very similar, as in this example with antelope horns:
