Abstract: An asymmetrical or relieved piston is provided in a fluid motor or a pump. The piston is rigidly connected to one end of the connecting rod, the opposite end of which is pivotally connected to a rotating crankshaft. The piston has a relieved upper and lower section each of which has a partial spherical surface. When the piston is tilted in one direction through half of a rotation of the crankshaft, a seal is formed between the partial spherical surface and the wall of a cylinder. During the other half of the rotation, the relieved piston is tilted in the opposite direction, the seal is broken, and fluid bypasses the piston from the upper half of the cylinder volume to the lower half or vice versa. A floating poppet valve is utilized in the engine, and a floating check valve is utilized in the pump of the described single piston embodiments.