Oscillating reciprocation is an action where a body's displacement 'reciprocates' in a given axis or defined displacement vector and 'oscillates' along that axis usually perpendicular to the defined displacement. eg. the new Sabre Saw

Sabre Saw

The sabre saw is a powered or unpowered hand-held reciprocating saw. The sabre saw consists of a reciprocating cutting implement, usually a toothed blade, to chiefly cut through wood and other various materials. its primary use is to slice material handily, rather than using the traditional...

's on the market are reciprocating saw

Reciprocating saw

A reciprocating saw is a type of saw in which the cutting action is achieved through a push and pull reciprocating motion of the blade.The term reciprocating saw is commonly assigned to a type of saw used in construction and demolition work...

's which also oscillate the blade in an up and down fashion perpendicular to the cutting stroke.