Position Analysis of a 4 bar RRRR Linkage Using Complex Numbers
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Position Analysis of a 4 bar RRRR Linkage Using Complex Numbers. Q. P. Im. q 3. q 4. q 2. q 1. Re. O. Viewing the point P from two directions in the complex plane. Position Analysis of a 4 bar RRRR Linkage Using Complex Numbers. Q. P. Im. q 3. q 4. q 2. q 1. Re. O.

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Q 1

Position Analysis of a 4 bar RRRR Linkage Using Complex Numbers

Q

P

Im

q3

q4

q2

q1

Re

O

Viewing the point P from two directions in the complex plane


Q 1

Position Analysis of a 4 bar RRRR Linkage Using Complex Numbers

Q

P

Im

q3

q4

q2

q1

Re

O

Separating the real

And the imaginary parts

We have two unknowns

And two scalar equations to solve for them


Q 1

Position Analysis of a 4 bar RRRR Linkage Using Complex Numbers

Q

P

Im

q3

q4

q2

q1

Re

O

Rearranging terms

Squaring and adding


Q 1

Position Analysis of a 4 bar RRRR Linkage Using Complex Numbers

Q

P

Im

q3

q4

q2

q1

Re

O

Rearranging terms

Rearranging further


Q 1

Position Analysis of a 4 bar RRRR Linkage Using Complex Numbers

Q

P

Im

q3

q4

q2

q1

Re

O

Substitute

And

To get

Or


Q 1

Position Analysis of a 4 bar RRRR Linkage Using Complex Numbers

Q

P

Im

q3

q4

q2

q1

Re

O

Solving

we get two roots!

And

The signs of sinq3 and cosq3 will let us determine the quadrant in which q3 lies


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