6.16 : Machines: Problem Solving I

A toggle clamp is a mechanical device commonly used for holding and clamping objects in various applications, such as woodworking, metalworking, and assembly operations. Consider a toggle clamp subjected to a force of 200 N at the handle. The vertical clamping force can be calculated, provided the dimensions of the toggle clamp are known.

The toggle clamp system is a machine structure consisting of movable, pin-connected multi-force members that form a stabilized system to transmit forces. The member CD is a two-force member, meaning that the collinear forces acting at both ends are equal in magnitude but opposite in direction.

A free-body diagram for the section BCF is considered to analyze the forces. The moment equilibrium condition is applied to the pivot pin B.

The result gives the force along member CD as 2185.64 N. Substituting the value of force along member CD in the horizontal force equilibrium condition, the force B_x is calculated as 1092.82 N.

Considering a free-body diagram for section EBA, the moment equilibrium condition is applied at joint A.

Substituting the value of the horizontal reaction force at B into the moment equilibrium equation, the value of the vertical clamping force at point E is calculated to be 728.55 N.