Determine the forces in the pistons of a hydraulicly operated excavator.

Equilibrium of a rigid body.  Find tension to raise a pole.

Determine the reactions supporting a cantilever beam carrying concentrated forces and moments.

Rigid body equilibrium problem.  Easiest to solve by replacing forces on the perimiter of the pulley with equivalent forces at the axle.

Classic problem of a vehicle parked on an incline.  Best solved by rotating the coordinate system.

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Determine the mechanical advantage of a pair of compound lopping shears.

An A-frame structure supporting a force and a moment. The feet are at the same vertical position, so taking moments at one foot yields the y component of the reaction at the other.

Classic machine problem.  Find the mechanical advantage of a pair of pliers and the force on the hinge pin.

A hand truck on wheels.  Easiest to solve by rotating coordinate system.

Two forces act on a bell crank. This problem has two unknown magnitudes and an unknown direction which makes it tricky to solve by the equilibrium equation method.  

The solution is much simpler if three force body principle is used.

Find the reactions of a rigid body (a truss) at a pin and roller.  All loads are either horizontal or vertical.

Find the reactions of a rigid body (a triangular plate) at a pin and roller.  The load is at an angle.

Find the forces in the members of a truss using the method of joints.