ME 321 Kinematics and Dynamics of Machines - Mechanical and ...

1.0 INTRODUCTIONME 321 – Kinematics and Dynamics of MachinesAll ‘Text References’ in these notes are for:Mechanism Design: Analysis and Synthesis, Volume 1, Fourth Edition, Erdman,Sandor and Kota, Prentice-Hall, 2001.Students should review the introductory chapter of the text.1.1 DefinitionsKinematics is the study of motion, without regard to forces. This is usually the first stepin the analysis or design of a mechanism.Kinetics is the study of forces on systems in motion. Dynamics is the combination ofkinematics and kinetics.A Mechanism is a combination of rigid or resilient bodies joined together to provide aspecific absolute motion.A machine is a mechanism capable of performing useful work or capable of transmittingsignificant forces.An engine is a machine which converts energy from one form to another.Links are rigid or flexible members have at least two nodes (points of attachment).Example links are:Binary link: Ternary link: Quaternary link:(2 nodes) (3 nodes) (4 nodes)Figure 1.1: Example link configurations.

ME 321 – Kinematics and Dynamics of Machines S. Lambert Winter 2002Curvilinear translation: points in the body move along identical curves, and so thelink does not rotate with respect to the ground (ex., link connecting two disks inFigure 1.3).Rotation: points in the body rotate about a single point, which is usually fixed to theground (ex., disks in Figure 1.3).General planar motion: a general combination of rotation and translation (ex.,connecting rod joining piston and disk in Figure 1.3).Figure 1.3: Example mechanism showing different types of planar motion.We classify linkages in terms of the number of links. A dyad, Figure 1.4, is two linkswith one joint, usually a pin joint. By itself, it does not usually constitute a usefullinkage, but the term is sometimes used to indicate parts of a more complex linkage. Inaddition, a dyad may be added to an existing linkage to transmit motion from a motor(rotation) to the linkage.Figure 1.4: Example dyad.Similarly, three links (a triad), Figure 1.6, can not usually be used alone to form a usefulmechanism. It either represents a part of a more complex mechanism, or a structure.Figure 1.5: Example traids.The most useful mechanism has four links – the four-bar mechanism. There are twobasic configurations. In one case, the four links are joined by 4 pin-joints. In the other3

ME 321 – Kinematics and Dynamics of Machines S. Lambert Winter 2002case, a slider joint replaces one of the pin joints. Schematic and simplified (skeleton)diagrams of each are shown in Figure 1.6.An mechanism inversion is said to occur when the fixed link is allowed to move, and analternative link is fixed. The relative motion between the links remains unchanged, butthe absolute motion, and the function of the mechanism is changed. This is mostdramatically seen in the various inversions of the slider-crank mechanism, Figure 1.7.Figure 1.6: Example four-bar linkage and slider crank.4

ME 321 – Kinematics and Dynamics of Machines S. Lambert Winter 2002Figure 1.7: Various inversions of the slider-crack mechanism, from top to bottom:conventional engine, rotary engine, quick-return mechanism, and pump.1.2 Degrees of FreedomText Reference: Degrees of freedom and Gruebler’s equation are covered in section1.7 of the text, pages 21-30.5

ME 321 – Kinematics and Dynamics of Machines S. Lambert Winter 2002By working with Gruebler’s equation, we can examine the possible combinations of linksand joints which we can use to form a mechanism with a specified number of degrees offreedom. Generally, we are after 1 dof.Consider a mechanism with 2 links. Since 1 link is assumed fixed, we start out with 3dof, and reduce this to 1 by adding a single pin or slider joint, Figure 1.8. This is not aparticularly useful mechanism, since we get out pretty much what we put in: a rotation inthe first case and a translation in the second case. Note that we could also use two rollsliderjoints to constrain the second link, as shown at right in Figure 1.8. This is notparticularly useful either.2211Figure 1.8: Example 2-bar mechanismsNow consider a mechanism with 3 links. In this case, we start out with 6 dof, and mustadd joints to constrain 5 dof to be left with 1 dof. This is possible with two pins and aroll-slider joint, since the latter only constrains 1 dof. This is an example of a camfollowermechanism. Replacing one of the pins with a slider results in the moreconventional cam-follower mechanism shown at right in Figure 1.9.313221 11Figure 1.9: Example 3-bar mechanisms.With four bars, and four pins, we get the standard 4-bar mechanism, Figure 1.10.Replacing one pin with a slider gives the slider-crank mechanism, Figure 1.10, and itsvarious inversions, Figure 1.7.8

ME 321 – Kinematics and Dynamics of Machines S. Lambert Winter 200223546234561 1Watt I1 1 1Watt IIFigure 1.12: Watt six-bar mechanisms (note that the ground is a ternary member for theWatt II mechanism.56623423 451 1Stephenson I1 1Stephenson II352461 2 3Stephenson IIIFigure 1.13: Stephenson six-bar mechanisms.10