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Question
Using constraint equations find the relation between a1 and a2.
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Solution
Point 1, 2 , 3 and 4 are movable. Let their displacements from a fixed line be x1,x2,x3 and x4
x1+x3=l1
(x1−x3)+(x4−x3)=l2
(x1−x4)+(x2−x4)=l3
On double differentiating with respect to time, we will get following three constraint relations
a1+a3=0 ...(i)
a1+a4−2a3=0 ...(ii)
a1+a2−2a4=0 ...(iii)
Solving Eqs. (i), (ii) and (iii), we get
a2=−7a1
Which is the desired relation between a1 and a2.
x1+x3=l1
(x1−x3)+(x4−x3)=l2
(x1−x4)+(x2−x4)=l3
On double differentiating with respect to time, we will get following three constraint relations
a1+a3=0 ...(i)
a1+a4−2a3=0 ...(ii)
a1+a2−2a4=0 ...(iii)
Solving Eqs. (i), (ii) and (iii), we get
a2=−7a1
Which is the desired relation between a1 and a2.
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