Deriving angles for a four bar linkage (vectors and complex numbers) I have been

Question

Deriving angles for a four bar linkage (vectors and complex numbers)

I have been trying to show justification for how I got theta 3 but I have gone wrong somewhere. I should be getting two answers, one a sin(theta3) =.... and one a cos(theta3)=.....

I am looking to get a complete process from where I have gone wrong

This vector loop can be summarised with the following equation: R1 R2 R3 R4 0 Equation 1 Each vector in this loop can be expressed in a complex exponential form which has a length as a magnitude and an angle for direction. Considering each vector has the following components: Vector Length The vectors can be expressed as: L1ejo R2 L2 ejo2 Lae LAej64 Subbing these values into equation 1 Laejo2 LAejos Equation 2 According to Euler's identity as outlined in equation 3, the above formula can then be expressed in complex polar form which can be used to create scalar equations Aetjo A(coso jsing) Equation 3 L1 L2(cos02 jsin02) 3 cos03 jsin03) L4 (cos04 jsino4 0 uation 4 This provides a real and imaginary component which both equate to zero.: La cos0. LA coso. COS Equation 5 (L2 sin02 L3 sin03 LA sino 00 Rearranging each component of equation 5 provides L1 L2 cos02 L4 cos04 L2 sin02 L4sino4 sin03 cos03 Applying trig identities to this equation makes it possible to isolate e3: sino L sin02 LASin0 tan 3 cos0. L1 L2 cos02 cos0

Explanation / Answer

From Equation (5), you can get,

Cos(thets3) = {L1 + L2cos (theta2) -L4cos(theta4)} / L3

Sin(thets3) = {L2sin(theta2) - L4 Sin(theta4)} / L3

This is the way you can get sin and cos values.. This is what I understood from your question..

Related Questions

Navigate

• Browse (All)
• Browse D
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.