Question

y S6 S5 QB 5 6 4 r13 A 2 Ao r2 q 3 r12 S3 r4 x r11 S4 Bo 1 

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y S6 S5 QB 5 6 4 r13 A 2 Ao r2 q 3 r12 S3 r4 x r11 S4 Bo 1

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University Physics with Modern Physics
University Physics with Modern Physics
Hugh D. Young 14th Edition
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The numerical value of the quick turn mechanism shown in the figure to do the kinematic analysis from the path. a) Obtain the constraint equations. b) Velocity and acceleration by determining the required matrices and vectors. Formulate analysis problems.
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Transcript

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00:01 Hello students in this question we are given a function b of sigma is equal to 1 minus sigma 2 times i which is a 3 by 3 matrix, right? plus 2 times sigma bar plus 2 times sigma times sigma transpose so we need to find the inverse function and we can use the identity sigma star the whole square is equal to sigma sigma t minus sigma square times i which is a 3 by 3 function so we can use the identity and we can rewrite the expression of b sigma so b sigma can be rewritten as b sigma is equal to 1 minus sigma 2 square times i plus 2 times sigma sigma transpose right 2 times sigma sigma transpose minus sigma square times i plus 2 sigma times again just write it there 2 sigma times sigma sigma transpose minus sigma square i now we can simplify this we can simplify this so b sigma will be equal to i minus sigma square sigma 2 square i plus 2 sigma sigma transpose minus sigma square 2 sigma square i plus 2 sigma and sigma transpose so that is 2 sigma square sigma transpose minus sigma cube times i times 2 will be there so b sigma can be simplified as these two terms right sigma square 2 sigma square sigma transpose is there so this will be the inverse of i will be equal to the i itself because it's a 3 by 3 function so it's an identity matrix minus the sigma you can take out sigma from here you can take out sigma from all here so you go sigma can be taken or we can take i from all of these things so i times sigma 2 square minus minus 2 sigma square minus 2 sigma cube right and then you can go ahead with the second function so that is equal to so this this minus becomes plus and this minus becomes again plus okay, plus the second term is sigma 2 sigma sigma t and here we have 2 them so sigma transpose can be taken outside so 2 sigma 2 sigma square, so this is the function so transpose b...
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