Dynamics of Mechanical Systems 2009 Part 8 docx
Dynamics of Mechanical Systems 2009 Part 8 docx
... will be on holonomic systems because, as noted earlier, the vast majority of mechanical systems of interest are holonomic systems. 11.4 Vector Functions, Partial Velocity, and Partial Angular Velocity Consider ... 355 The number of degrees of freedom of a mechanical system is the number of coordinates of the system if it were unrestricted minus the number of constra...
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Dynamics of Mechanical Systems 2009 Part 4 docx
... defined as: (5 .8. 18) Then, Eqs. (5 .8. 16) and (5 .8. 17) become: (5 .8. 19) and (5 .8. 20) Solving for ξ and η we obtain: (5 .8. 21) (5 .8. 22) where ∆, the determinant of the coefficients, is: (5 .8. 23) xx xy CQ QQ =+ − + ωα αω 2 24 ˙˙ ˙˙ yy xy CQ QQ =+ + + αω αω ˙˙ ˙˙ 2 24 xx yy ... 13 223 0 3 10 4 15 3 8 4 8 0 12 12 16 30 60 24 32 1131 144 192−+nn Mnnn O =−−160 30 1 68 12 3 ftlb...
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Dynamics of Mechanical Systems 2009 Part 13 docx
... as: ( 18. 5.14) where the are: ( 18. 5.15) Finally, by using Eq. ( 18. 5.12) we may solve Eq. ( 18. 5.15) for the in terms of the as: ( 18. 5.16) Equation ( 18. 5.16) is analogous to Eqs. ( 18. 5 .8) , ( 18. 5.9), ... transpose; that is, ( 18. 3.5) Hence, from Eq. ( 18. 3.4) we have: ( 18. 3.6) In view of Eqs. ( 18. 3.4), ( 18. 3.5), and ( 18. 3.6), we can rewrite Eq. ( 18. 3.1) in the si...
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Dynamics of Mechanical Systems 2009 Part 15 docx
... 9:07 AM 684 Dynamics of Mechanical Systems motion of the system. Expressed another way, the robot has (n – 6) more degrees of freedom than needed to uniquely determine the movement of the system. ... desired motion of the last link. AfF ˙˙ γ= + FF ll = ′ 0593_C19_fm Page 684 Tuesday, May 7, 2002 9:07 AM 690 Dynamics of Mechanical Systems systems. For an actual robot,...
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Dynamics of Mechanical Systems 2009 Part 1 ppsx
... Inertia Torques 2 28 References 230 Problems 230 Chapter 8 Principles of Dynamics: Newton’s Laws and d’Alembert’s Principle 241 8. 1 Introduction 241 8. 2 Principles of Dynamics 242 8. 3 d’Alembert’s ... d’Alembert’s Principle 243 8. 4 The Simple Pendulum 245 8. 5 A Smooth Particle Moving Inside a Vertical Rotating Tube 246 8. 6 Inertia Forces on a Rigid Body 249 8. 7 Proj...
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Dynamics of Mechanical Systems 2009 Part 2 potx
... different. Example 2 .8. 2: Validity of Eqs. (2 .8. 6) and (2 .8. 7) and the Necessity of Parentheses Verify Eqs. (2 .8. 6) and (2 .8. 7) using the vectors of Eq. (2 .8. 7). Solution: From Eqs. (2 .8. 2) and (2 .8. 9), A ... sum of products of the elements of the ith row of A with the corresponding elements of the jth column of B. Specifically, (2.10.5) where n is the number...
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Dynamics of Mechanical Systems 2009 Part 3 pptx
... 84 Dynamics of Mechanical Systems Observe that θ measures the rotation of B in R. It is also a measure of the orientation of B in R. In this context, the angular velocity of B in R ... May 6, 2002 2:06 PM 126 Dynamics of Mechanical Systems Using polar coordinates the constraint equation is: (5.2.2) The number of degrees of freedom of a mechanical system...
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Dynamics of Mechanical Systems 2009 Part 5 pps
... definition of equivalent force systems, W and T are: (6 .8. 8) and (6 .8. 9) where k is a downward-directed unit vector as in Figure 6 .8. 4 and M is the total mass of particles of B. The last equality of ... P6 .8. 1 Masses and Coordinates of a Set of Particles P i m i x i y i z i P 1 6 –102 P 2 43–74 P 3 34–5 –5 P 4 88 07 P 5 1 –2 –3 –9 P 6 91–20 P 7 47 83 P 8 5 –34–2 P 9 51...
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Dynamics of Mechanical Systems 2009 Part 6 pdf
... have: (8. 7.15) Equation (8. 7.5) then takes the form (see Eqs. (8. 6.10) to (8. 6.12)): (8. 7.16) (8. 7.17) (8. 7. 18) These equations form a system of nonlinear differential equations. A simple solution of the ... Page 2 38 Monday, May 6, 2002 2:42 PM 2 58 Dynamics of Mechanical Systems 8. 10 Double-Rod Pendulum As an extension of the foregoing system, consider the dou...
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Dynamics of Mechanical Systems 2009 Part 7 pps
... Dynamics of Mechanical Systems The left side of Eq. (10.6.2) may be recognized as the power of F (see Eq. (10.4.2)). The right side of Eq. (10.6.2) may be expressed in terms of a derivative of ... ˆ ΩΩΩΩΩΩΩΩ= () = 28 28 or 0593_C09_fm Page 310 Monday, May 6, 2002 2:50 PM 282 Dynamics of Mechanical Systems where the final expression is obtained by recognizing...
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