but no amount of axial load force against the shaft will cause it to turn backwards. In an inclined plane, a load can be pulled up the plane by a sideways input force, but if the plane is not too steep and there is enough friction between load and plane, when the input force is removed the load will remain motionless and will not slide down the plane, regardless of its weight. A wedge can be driven into a block of wood by force on the end, such as from hitting it with a sledge hammer, forcing the sides apart, but no amount of compression force from the wood walls will cause it to pop back out of the block. A machine will be self-locking if and only if its efficiency is below 50%: Whether a machine is self-locking depends on both the friction forces (coefficient of static friction) between its parts, and the distance ratio (ideal mechanical advantage). If both the friction and ideal mechanical advantage are high enough, it will self-lock. Proof When a machine moves in the forward direction from point 1 to point 2, with the input force doing work on a load force, from conservation of energy the input work is equal to the sum of the work done on the load force and the work lost to friction If the efficiency is below 50% From When the machine moves backward from point 2 to point 1 with the load force doing work on the input force, the work lost to friction is the same So the output work is Thus the machine self-locks, because the work dissipated in friction is greater than the work done by the load force moving it backwards even with no input force. Modern machine theory Machines are studied as mechanical systems consisting of actuators and mechanisms that transmit forces and movement, monitored by sensors and controllers. The components of actuators and mechanisms consist of links and joints that form kinematic chains. Kinematic chains Simple machines are elementary examples of kinematic chains that are used to model mechanical systems ranging from the steam engine to robot manipulators. The bearings that form the fulcrum of a lever and that allow the wheel and axle and pulleys to rotate are examples of a kinematic pair called a hinged joint. Similarly, the flat surface of an inclined plane and wedge are examples of