The word jog originated in England in the mid-16th century. The etymology of the word is unknown, but it may be related to shog or have been a new invention. In 1593, William Shakespeare wrote in Taming of the Shrew,
“you may be jogging whiles your boots are green”.
At that point, it usually meant to leave.
The term jog was often used in English and North American literature to describe short quick movements, either intentional or unintentional. It is also used to describe a quick, sharp shake or jar. Richard Jefferies, an English naturalist, wrote of “joggers”, describing them as quickly moving people who brushed others aside as they passed. This usage became common throughout the British Empire, and in his 1884 novel My Run Home, the Australian author Rolf Boldrewood wrote, “Your bedroom curtains were still drawn as I passed on my morning jog”.
So if the sight of a jogger jogging in the park jogs your memory, that too is thoroughly appropriate. To jog also meant to jerk. So if your memory receives a jolt, it is jogged, as in the tract of 1778: An Antidote to Popery; or, the Protestant’s Memory jogg’d in Season.
However, if what happens if you jerk and jolt yourself repeatedly? Well, obviously you could just add the frequentative suffix -le and get joggle. But you might find yourself moving along in little jolts, or as Dr Johnson put it in his dictionary:
Jog: to move with small shocks like those of a low trot.