Mechanical Engineers Handbook 2011 Part 5 potx

The forces acting on the system include a driving torque M, an external driven force F, and the forces transmitted from the frame atkinematic pair A, F01, and at kinematic pair C, F03..

4.3 Free-Body Diagrams

A free-body diagram is a drawing of a part of a complete system, isolated inorder to determine the forces acting on that rigid body The following forceconvention is de®ned: Fij represents the force exerted by link i on link j

Figure 4.4 shows various free-body diagrams that can be considered inthe analysis of a crank slider mechanism (Fig 4.4a)

In Fig 4.4b, the free body consists of the three moving links isolatedfrom the frame 0 The forces acting on the system include a driving torque M,

an external driven force F, and the forces transmitted from the frame atkinematic pair A, F01, and at kinematic pair C, F03 Figure 4.4c is a free-bodydiagram of the two links 1 and 2 Figure 4.4d is a free-body diagram of asingle link

The force analysis can be accomplished by examining individual links orsubsystems of links In this way the reaction forces between links as well asthe required input force or moment for a given output load are computed.

4.4 Reaction Forces

Figure 4.5a is a schematic diagram of a crank slider mechanism comprising of

a crank 1, a connecting rod 2, and a slider 3 The center of mass of link 1 is

C1, the center of mass of link 2 is C2, and the center of mass of slider 3 is C.The mass of the crank is m1, the mass of the connecting road is m2, and themass of the slider is m3 The moment of inertia of link i is ICi, i ˆ 1; 2; 3.The gravitational force is Gi ˆ ÿmig , i ˆ 1; 2; 3, where g ˆ 9:81 m=s2

is the acceleration of gravity

For a given value of the crank angle f and a known driven force Fext, thekinematic pair reactions and the drive moment M on the crank can becomputed using free-body diagrams of the individual links

Figures 4.5b, 4.5c, and 4.5d show free-body diagrams of the crank 1, theconnecting rod 2, and the slider 3 For each moving link the dynamicequilibrium equations are applied

For the slider 3 the vector sum of the all the forces (external forces Fext,gravitational force G3, inertia forces Fin 3, reaction forces F23, F03) is zero(Fig 4.5d):

M…2†B ˆ …rC ÿ rB†  F32‡ …rC 2ÿ rB†  …Fin 2‡ G2† ‡ Min 2ˆ 0;

orP

‡

k

xC 2ÿ xB yC 2ÿ yB 0

ÿm2xC 2 ÿm2yC 2ÿ m2g 0

‡

k

xC 4ÿ xE yC 4ÿ yE 0

... from the set of eightequations (4.19), (4.20), (4.21), (4.22), (4.23), (4.24), (4. 25) , and (4.26)

4 .5 Contour Method

An analytical method to compute reaction forces that... kinematic pair

Figure 4.6