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Downloaded from Digital Engineering Library @ McGraw-Hill (www.digitalengineeringlibrary.com) Copyright 2004 The McGraw-Hill Companies. All rights reserved. Any use is subject to the Terms of Use as given at the website.

The driven link d will be at angle = cos 1 where h2 = a2 + b2 + 2ab cos The transmission angle will be = cos 1 c2 + d 2 a2 b2 2ab cos 2cd (3.10) (3.9) h2 + d 2 c2 h2 + a2 b2 + cos 1 2hb 2hd (3.8)

A point on coupler P has coordinates Px = b cos + r cos ( + ) Py = b sin + r sin ( + ) (3.11)

@interface BBParticleSystem : BBSceneObject { NSMutableArray * childrenParticles; GLfloat * uvCoordinates; GLfloat * vertexes; NSMutableArray * unusedParticles; NSInteger vertexIndex; BOOL emit; CGFloat emitCounter; BBRange emissionRange; BBRange sizeRange; BBRange growRange;

goto loop 'output the msg1_o: x3 = tabl + x4 = msc1 + goto msg_o msg2_o: x3 = msc1 + x4 = msc1 + goto msg_o msg3_o: x3 = msc1 + x4 = msc1 + goto msg_o msg4_o: x3 = msc1 + x4 = msc1 +

3.6.2 Velocity and Acceleration The velocity of the point on the coupler can be expressed as d dPx d =b sin r sin ( + ) dt dt dt dPy d d =b cos + r cos ( + ) dt dt dt (3.12)

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Downloaded from Digital Engineering Library @ McGraw-Hill (www.digitalengineeringlibrary.com) Copyright 2004 The McGraw-Hill Companies. All rights reserved. Any use is subject to the Terms of Use as given at the website.

As you can see, the mathematics gets very complicated very rapidly. If you need to establish velocity and acceleration data, consult Ref. [3.1], [3.7], or [3.11]. Computer analysis is based on the closed vector loop equations of C. R. Mischke, developed at Pratt Institute in the late 1950s. See [3.19], Chap. 4.

3.6.3 Dynamic Behavior Since all linkages have clearances in the joints as well as mass for each link, highspeed operation of a four-bar linkage can cause very undesirable behavior. Methods for solving these problems are very complex. If you need further data, refer to numerous theoretical articles originally presented at the American Society of Mechanical Engineers (ASME) mechanism conferences. Many have been published in ASME journals.

BBRange xVelocityRange; BBRange yVelocityRange; BBRange zVelocityRange; BBRange lifeRange; BBRange decayRange; CGFloat CGFloat CGFloat CGFloat } minU; maxU; minV; maxV;

Listing 12-1

3.7.1 Two Positions of a Plane The line AiBi defines a plane (Fig. 3.8) which is to be the coupler of the linkage to be designed. When two positions are defined, you can determine a particular point, called the pole (in this case P12, since the motion goes from position 1 to position 2). The significance of the pole is that it is the point about which the motion of the body is a simple rotation; the pole is seen to be the intersection of the perpendicular bisectors of A1A2 and B1B2. A four-bar linkage can be created by choosing any point on a1a2 as OA and any reasonable point on b1b2 as OB. Note that you do not have a totally arbitrary choice for the fixed pivots, even for this elementary case. There are definite limitations, since the four-bar linkage must produce continuous motion between all positions. When a fully rotating crank is sought, the Grubler criterion must be adhered to. For double-rocker mechanisms, the particular link lengths still have definite criteria to meet. You have to check these for every four-bar linkage that you design.

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