Question

y D 4 e C 3 O s r2 ? 2 ? x A0 r1 B0 1

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y
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r1
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University Physics with Modern Physics
University Physics with Modern Physics
Hugh D. Young 14th Edition
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In the figure, arm-sledge has dimensions r1 = 50 cm, r2 = 25 cm, and ℓ = 80 cm. The A0C arm of the mechanism rotates with a constant angular velocity of ω = φ = 4 rad/s. a) Find the position and speed of limbs 3 and 4 analytically at the location defined by φ = 60° by performing the kinematic analysis. b) Obtain the constraint equations of the mechanism. c) With the aid of the numerical path-specific formulation for the position in (a), find the speed and acceleration of θ, θ', s', and s'' by performing the acceleration analysis. d) Calculate the velocity coefficient and velocity of point D. y 4 e 2 0 .X Ao r1 Bo 1
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Transcript

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00:01 Hello students, according to this question we are going to find the acceleration.
00:06 Before that we are going to consider the r value.
00:08 R is equals to k theta.
00:12 After differentiation we will get r dash is equals to k theta dash.
00:19 Again we are going to differentiate so that we get r double dash is equals to k alpha.
00:27 Now double dash is equals to alpha.
00:31 We are going to consider double dash as an angular acceleration.
00:37 Now theta dash is equals to alpha t plus c1.
00:45 We are going to consider c1 value.
00:47 Poisson value is equals to zero.
00:49 So we will end up with theta dash is equals to alpha t.
00:54 Now we are going to integrate this value so that we get theta is equals to theta t square by 2 plus c2.
01:05 Here we are going to substitute c2 value as pi by 4.
01:10 So we get theta is equals to alpha t square by 2 plus pi by 4.
01:19 Now we know that now we are going to consider theta is equals to 3 pi by 4.
01:29 Now we are going to substitute this value 3 pi by 4 is equals to alpha t square by 2 plus pi by 4...
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