Putting your shoulder to the wheel means to put full effort into the task until it is completed, to work persistently and wholeheartedly. We have several phrases that have a similar meaning in English. This is a very common expression.
The image is that of an old-fashioned farm wagon or cart that has become stuck in the mud. The way to get the thing to move is to push it, and one would literally put one's shoulder against the wheel in order to give the most force to the effort.
The metaphor is from helping to push a cart or carriage when it has become stuck in the mud or a pothole, a task requiring strenuous effort. One of the other synonymous phrases referred to is "nose to the grindstone" and houswives sometimes complain of "working their fingers to the bone".
If one has not been seen to make suffiicient effort one may be informed that one had better "get your finger out!". Where the finger has so far thought to have been lodged, I leave my fellow foreros to speculate.
This thread has become a list of equivalents, not an explanation of the thread topic.
It has therefore been closed.