I think Leonardo would have liked Shiva, a ridable mechanical tiger made by Kezanti (Dirk Dewulf) of Brugge; Tippoo's Tiger, currently in the V&A; and the many automata of John Joseph Merlin and James Cox, who
... opened shops in Canton where mandarins could acquire mechanical clocks, mobile elephants, and automatic tigers ...
- The sciences in enlightened Europe, William Clark, Jan Golinski, Simon Schaffer, University of Chicago Press, 1999
Obligatory book connection: Kit Reed, who I'm pleased to see is still extant, as she was one of the authors who got me reading SF. One of the first SF stories I remember was her 1964 "Automatic Tiger" - about a man who achieves temporary self-worth through owning a robot tiger. He buys it as a gift to ingratiate himself with a rich relative, but on opening the box to test it decides to keep it.
It came in a medium-sized box with an orange-and-black illustration and the words "ROYAL BENGAL TIGER" in orange lettering across the top ...
.... As the sides fell away he dropped his hands, disappointed at first by the empty-looking heap of fur. The fur had a ruggy look, and for a minute he wondered if the packers at the factory had made a mistake. Then, as he poked it with his toe he heard a click and the steel frame inside the fur sprang into place and he fell back, breathless, as the creature took shape.
It was a full-sized tiger made from a real tiger-skin skilfully fitted to a superstructure of tempered metal so carefully made that the beast looked no less real than the steely-limbed animals Benedict had seen at the city zoo. Its eyes were of amber, ingeniously lit from behind by small electric bulbs, and Benedict noted hysterically that its whiskers were made of stiff nylon filament. It stood motionless in an aura of jungle-bottom and power, waiting for him to find the microphone and issue a command. An independent mechanism inside it lashed the long, gold-and-black striped tail. It filled half the room.
Awed, Benedict retreated to his couch and sat watching the tiger. Shadows deepened and soon the only light in the room came from the creature's fierce amber eyes.
(I've tracked it to the anthology where I first read it: The 10th Annual of the Year’s Best S-F, 1965, ed. Judith Merril, which also contained Norman Kagan's brilliant The Mathenauts). Kit Reed's artist husband Joseph W Reed later painted this illustration: Automatic Tiger (1973).
PS: Some examples on a more bijou scale. On eBay, there are currently pictures of an 1890s Leaping Tiger automaton by Roullet & Decamps. The same company also produced automata of cats - see The Automata / Automaton Blog - that might be viewed as the precursors of robot cats such as Sega Toys' Yume-Neko Smile.