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For example, could a Yuan-ti with a snake tail instead of legs still use the jump skill?

I am specifically asking about creatures without legs who still have some mode of land-based locomotion, e.g. a Yuan-ti's or Lillend's tail, rather than humanoid characters who have somehow lost their legs.

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The skill description is silent about that

There are no anatomical pre-requisites for the use of the Jump skill written directly into the description, only requiring a running start and a (land) movement speed, so you can use the skill properly. This may be an answer to your question:

You can use the jump skill, as long as you have land movement speed. It makes no sense to jump while flying or swimming.

So, by RAW, I don't see anything limiting a snake-like character to jump. Of course, like the other answer pointed out, a race can have a inherent jump limitation, but that's too specific to broaden to what you are going for, I believe.

Either that, or the Monster Manual tries to put some sense into elephants jumping:

Monster Manual pg 7:

Natural Tendencies: Some creatures aren't made for certain types of physical activity. Elephants, despite their great Strength scores, are terrible at jumping. Giant crocodiles, despite their high Strength scores, don't climb well. Horses can't walk tightropes. If it seems clear to you that a particular creature simply is not made for a particular physical activity, you can say that the creature takes a -8 penalty on skill checks that defy its natural tendencies. In extreme circumstances (a porpoise attempting a Climb check, for instance) you can rule that the creature fails the check automatically.

Anyway, this gets a little more complicated when you start to consider severed limbs that were previously used to jump:

  • Do you have that in your game? How do you deal with that?
  • Where does the movement speed comes from, anatomically?

Again, the core RAW is not enough to answer those two questions, and even including supplements, I believe the later one is never answered given the level of granularity for D&D.

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  • \$\begingroup\$ Maybe try and picture Lt. Dan from Forrest Gump? \$\endgroup\$ – FrancisJohn Jun 13 '16 at 10:33
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    \$\begingroup\$ I'll search for that on my MM and add to this as soon as I have time. \$\endgroup\$ – Punkgeon Jun 13 '16 at 13:44
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    \$\begingroup\$ @gaynorvader Thanks for quotation, it makes things much more clear (also, it seems like I forgotten "In extreme circumstances..." - heh, to think of it it's hilarious - I remember a game where a regiment of war elephants climbed vertical rocks, ladders and castlewalls... now I see we did it wrong... it was fun ^ ^) \$\endgroup\$ – Jaiden Snow Jun 13 '16 at 17:55
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    \$\begingroup\$ "It makes no sense to jump while flying or swimming." So fish and dolphins are incapable of jumping? \$\endgroup\$ – Michaellogg Jun 13 '16 at 19:15
  • \$\begingroup\$ @MikeKellogg good point, even if I would just consider that part of a swimming movement action. \$\endgroup\$ – Punkgeon Jun 13 '16 at 19:17
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Characters with different anatomies use those anatomies according to the same rules. Yuan-ti can, indeed, jump, as can everything else that can move unless it explicitly says that it cannot. An individual race could easily say that it cannot jump, or only jump at a penalty, but that is up to the individual race. Yuan-ti themselves have no such restrictions or limitations in their description, so they can just just the same as legged races.

And several snake species are quite good at jumping, so this isn’t completely unreasonable.

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  • \$\begingroup\$ Never saw snakes jump too far (compared to feats that small cats achieve) but... jumping fantasy snake doesn't feel like something unreasonable. Nature is weird. For example there are trap-jaw ants ( en.wikipedia.org/wiki/Odontomachus ) that can jump backwards using stored the energy of their jaws. Other ants can't jaw-jump because their muscles aren't wired that way. So - who knows what type of muscles and bones compose the tail of yuan-ti? \$\endgroup\$ – Jaiden Snow Jun 13 '16 at 13:49
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I'm willing to accept that Yuan-ti could jump, though I think they would have to suffer a penalty.

Most typical jumping creatures (humans, cats, etc) have joint design that allows them to gain mechanical advantage. They have to propel their entire bodies into the air; that requires a lot of force. The design of our feet includes levers that allow us to change the direction of a force, making it easier to jump. Cats are even better prepared for this; their small toes and long feet transfer more efficiently. The force is applied on the toes, the fulcrum just behind the toes, and the distance fulcrum to heel is long in comparison, making their jump require less force.

A yuan-ti, or Rattly, is jumping in the shape of a spring. Unfortunately this shape will provide no such mechanical advantage to lifting oneself in the air unless they were naturally wound. He is not naturally elastic. Since a snake doesn't have a compressed resting state, they have to provide all of the force to resist gravity. Even though the yuanti are relatively light, at least compared to humans, they should probably 'jump' at a penalty.

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