Mass is a property of objects proportional to the amount of force required to change their momentum (or, how heavy they are). There is no way to truly quantify mass in Besiege in real-world units; the density of blocks is both inconsistent and unaffected by scale. It is possible for a human-sized puppet, a plane, and a battleship to have the same mass.
Apart from that, mass obeys real-world physical laws. Mostly.
Most objects in Besiege have a set mass (most of which can be derived using mods, or found on their wiki pages). A handful of blocks and objects have adjustable mass, such as Ballast, Scaling Blocks, and Primitives.
Rigidity is a property of objects defining how much flex and stretch their connections have. It is limited to trigger connections between blocks and a handful of objects.
Rigidity is proportional to the mass and scale (per axis) for both sides of the connection. The higher these values are, so too will be the rigidity.
- A Brace has high rigidity; its connections are more likely to snap then to bend.
- A low-mass Ballast has low rigidity; its connections are much more flexible and forgiving.
The nature of rigidity in Besiege is the main reason why mechanical systems (particularly those involving Cogs) are imprecise; real-world mechanisms typically take it for granted that joints will not flex and that precision will be much tighter.
It is possible to take advantage of the much greater connection flex in Besiege - this is what Toring is all about.
Elasticity has not been mathematically defined yet; it is theorised that there is a small constant term involved (which is particularly apparent when Zero-Mass is involved).