Shawn Kenny, Ph.D., P.Eng. Assistant Professor Faculty of Engineering and Applied Science Memorial University of Newfoundland ENGI 1313 Mechanics I Lecture 35: Analysis of Frames and Machines

ENGI 1313 Statics I – Lecture 35© 2007 S. Kenny, Ph.D., P.Eng. 2 Lecture 35 Objective to illustrate the analysis of frames and machines by example

ENGI 1313 Statics I – Lecture 35© 2007 S. Kenny, Ph.D., P.Eng. 3 Example The compound shears are used to cut metal parts. Determine the vertical cutting force exerted on the rod R if a force of F = 20 lb is applied at the grip G. The lobe CDE is in smooth contact with the head of the shear blade at E.

ENGI 1313 Statics I – Lecture 35© 2007 S. Kenny, Ph.D., P.Eng. 4 Example (cont.) Draw FBD  GBA  CDE  FRE F = 20 lb F BC AxAx AyAy NENE DxDx DyDy FxFx FyFy NRNR NENE

ENGI 1313 Statics I – Lecture 35© 2007 S. Kenny, Ph.D., P.Eng. 5 Example (cont.) What FBD and Equilibrium Equations? F = 20 lb F BC AxAx AyAy NENE DxDx DyDy FxFx FyFy NRNR NENE

ENGI 1313 Statics I – Lecture 35© 2007 S. Kenny, Ph.D., P.Eng. 6 Example (cont.) GBA F = 20 lb F BC AxAx AyAy

ENGI 1313 Statics I – Lecture 35© 2007 S. Kenny, Ph.D., P.Eng. 7 Example (cont.) CDE F BC NENE DxDx DyDy

ENGI 1313 Statics I – Lecture 35© 2007 S. Kenny, Ph.D., P.Eng. 8 Example (cont.) FRE FxFx FyFy NRNR NENE

ENGI 1313 Statics I – Lecture 35© 2007 S. Kenny, Ph.D., P.Eng. 9 Example The kinetic sculpture requires that each of the three pinned beams be in perfect balance at all times during its slow motion. If each member has a uniform weight of 2 lb/ft and length of 3 ft, determine the necessary counterweights W1, W2, and W3 which must be added to the ends of each member to keep the system in balance for any position. Neglect the size of the counterweights.

ENGI 1313 Statics I – Lecture 35© 2007 S. Kenny, Ph.D., P.Eng. 10 Example (cont.) FBD AA BB CC  Angles? W1W1 AyAy LL AyAy ByBy W2W2 LL CyCy ByBy W3W3 LL  

ENGI 1313 Statics I – Lecture 35© 2007 S. Kenny, Ph.D., P.Eng. 11 Example (cont.) Beam A W1W1 AyAy LL 

ENGI 1313 Statics I – Lecture 35© 2007 S. Kenny, Ph.D., P.Eng. 12 Example (cont.) Beam B AyAy ByBy W2W2 LL 

ENGI 1313 Statics I – Lecture 35© 2007 S. Kenny, Ph.D., P.Eng. 13 Example (cont.) Beam C CyCy ByBy W3W3 LL 

ENGI 1313 Statics I – Lecture 35© 2007 S. Kenny, Ph.D., P.Eng. 14 References Hibbeler (2007) mech_1