THERE are many fascinating things stored on the shelves of the National Museums’ Collections Centre in Granton. Bronze age swords, mediaeval reliquaries, preserved biological specimens. I once saw a giant squid that had been washed ashore in the Forth, carefully folded up like a piece of laundry. There are skeletons too, amongst the pickled fauna and paper-wrapped archaeology. It is, the museum tells me, largely skeletons that they now collect from zoos and safari parks, often helping with post-mortem research on the bones that has even resulted in guidance on how best to house living animals.

But sometimes the museum’s taxidermy specialists have their day. It is here that the museum has its workshops, and it is in these spaces that specialists have been working on more than 60 superb taxidermy specimens – all from zoo animals who died of natural causes – for the Museum’s latest exhibition, a natural history investigation into our closest relations, the primates.

We share many things with apes, not least DNA – a somewhat staggering 99% with chimps and 98% with gorillas. Even our skulls have a passing resemblance as the "family tree" at the beginning of this exhibition shows. Here they are, from the fossilised remains of a small ape-like creature some 66 million years ago through evolutionary digressions and dead ends, albeit a few million years a pop, to the great apes and monkeys and humans we recognize today.

This is a family-friendly exhibition, a mix of immaculately prepared taxidermy and interactive exhibits. There are the screen-based terminals like “monkey supermarket” (match the monkey with its food) to a physical game in which you poke sticks into a termite hill to try and catch termites like a chimp. There is also a “jungle frame” in the centre of the exhibit for children aged 4-15 to practice their gibbon brachiation (swinging along using only your arms) or orangutan balancing. The only danger here is that you may have trouble getting the kids round the rest of the exhibition, but the taxidermy is a hit too.

Because there are fascinating creatures here. The animals are arranged in tableaux throughout the exhibition, each thematically treated, each animal presented in naturalistic action, from chimps cracking nuts with rocks to a fierce baboon racing along the forest floor. A Columbian black spider monkey with its glossy prehensile tail; a big-eyed Aye Aye poking through bark to get to a juicy grub with its curiously long claw-like fingers. Javan Langurs have the best hair (think stressed out parent crossed with finger in the electricity socket volume) and Emperor Tamarins superb moustaches. The Geoffroy’s Marmoset is a gorgeously glossy small animal whose russet hairs look almost like feathers. The variety is immense.

There are exhibits on the evolution of different body parts, the biology of sound, the difference in colour vision between species – even, amazingly between male and female of the same species. The space is divided by rainforest images against a persistent rainforest soundtrack, which throngs to the intermittent sound of piercing monkey alarm calls or aggressive guttural snarls. It can feel a little intimidating, which is presumably exactly what the monkeys intended.

Facts stand out and stay with you. The Douroucalis is the only nocturnal monkey and its skull has the huge eye sockets to prove it. Fat-tailed Dwarf Lemurs – tiny, tiny things – hibernate for up to 8 months, living off the fat in their eponymous tails, to survive the dry season. Gibbons have arms longer than their legs – all the better for brachiating with – whilst Lemurs have legs longer than their arms, like a sort of built-in springboard for making vertical leaps through the trees.

The visceral reality of some monkey life is left in the bush in this exhibition – thankfully so, or it would not be suitable for young families – but it is implied in the noises and sounds. And what is left – the stuffed specimens, the "be a monkey" games – subtly encourages interest without alienation. Because, most chillingly of all, as the latter part of this exhibition makes clear, half of all primate species are threatened with extinction, entirely through the actions of their closest living relatives. Us.

Monkey Business is at the National Museum of Scotland, Chambers Street, Edinburgh until April 23.

www.nms.ac.uk