To provide a complete wheel connecting assembly, facilitating integration with a vehicle, and moreover providing a suspension effectively controlling elastic and damping characteristics.

A suspension assembly for an automobile has a tire 1 fitted to a rim 10, and the assembly has a wheel carrier 3 and a guide member 6 for guiding the axial direction movement of the wheel carrier to supporting members 5. The supporting members has a journal 50 for fitting them to the chassis of a vehicle. The wheel carrier slidly is fitted to the guide member and moves within the guide member by using eight rollers 64 rotating on a guiding track 41 and 42, for instance arranged in the bar 4. The assembly has a spring 80 fitted between two collars 81 and 82, and an electric machine device 87 operable for controlling the movement of the displacement of a suspension.