Is there a CAD format, which allows to describe mechanical bonds between objects (axes, joints, springs, etc.) and/or motion of objects ?
CAD mechanical bonds and kinematics
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I don't have any personal CAD experience, but 3D objects can be defined using edges and nodes/vertices which reduces the problem to a graph-representation issue. 3D models defined using other techniques (such as composed functions or a filter pipeline, such as B-spline > Lathe or extrude > Transformation > Material/texture) will have considerably different means of serialization to file.
Storing motion is a separate issue entirely - and also complicated by the many different ways to represent animation, and if your system uses any kind of skeletal basis or solid-body physics/animation. Then there's keyframed and parameterised animation. Are you using an inverse-kinematics system too?
You need to be more specific about why you need such CAD format? Without really knowing what you are after, I think the closer thing to what you are asking for is Finite Element analysis programs like ANSYS, ABAQAS, etc. They work in CAD like environment and allow adding many types of elements to simulate dynamic (motion) anaylses and many other type of analysis. They include a huge variety of elements like linear springs are rltational springs.. etc.