A planetary gear train has four gears and one carrier. Angular velocities of the gears are $${\omega _1},{\omega _2},{\omega _3},$$ and $${\omega _4}$$ respectively. The carrier rotates with angular velocity $${\omega _5}.$$

What is the relation between the angular velocities of Gear $$1$$ and Gear $$4$$?

The number of inversions for a slider crank mechanism is

For a four bar linkage in Toggle position, the value of mechanical advantage is

In a four-bar linkage, $$S$$ denotes the shortest link length, $$L$$ is the longest link length, $$P$$ and $$Q$$ are the lengths of other two links. At least one of the three moving links will rotate by $${360^ \circ }$$ if