Forces and Moments: Part 7

Reduction to a wrench:

In the general case, the resultant moment (M_Ro) is perpendicular to F_R.

Now consider the case where F_R acts at an angle θ to M_Ro (Fig. a). Resolve M_Ro into two components (Fig. a):

M_|| || F_R and M_┴ ┴F_R,

Eliminate M_┴ by moving F_R by distance d = M_┴/ F_R from point O to point P. Now we are left with F_R at P and M_|| at O (Fig. b). Since M_|| is a free vector which can be moved to P (Fig. c)

This combination of a collinear force and a couple moment is called a wrench or screw.

The axis of the wrench has the same line of action as the force. The wrench tends to cause both translation along and rotation about this axis.

(a)

(b)

(c)