Kinematic Analysis & Synthesis - FC

Position Analysis

First, initial prototype was measured to start kinematic analysis. Afterwards the mechanism was broken into two separate four bar linkages and MATLAB was used to conduct the remainder of the kinematic analysis. Positional Analysis was conducted in two parts: position analysis for first four bar mechanism with input angle as θ₂, and position analysis for second four bar mechanism. From position analysis we get:

                                                           Figure 1: Position Analysis for four bar 1                                                                                                                                    Figure 2: Position Analysis for four bar 2

e = √(c² + d²)

θ_2,1 = arcsin(^c⁄_e)

θ_2,2 = θ₂ - θ_2,1

b₁ = √(a² + e² - 2ae*cos(θ₂))

θ₃ = arctan(^{(a*sin(θ₂)-c)} ⁄_{(a* cos(θ2) -d)})

θ₅ = arccos(^{(d₂ - a₂*cos(θ₃))}⁄_b2 )

c₂ = -a₂*sin(θ₃) - b₂*sin(θ₅)

Velocity Analysis

To get the velocity analysis, I took the time derivative of the position analysis. From velocity analysis, we get:

V_b = ω₂∗a∗(sin(θ₂)cos(θ₃) - cos(θ₂)sin(θ₃))

ω₃ = ^{(V_bcos(θ₃) - ω₂∗a∗sin(θ₂))}⁄(b∗sin(θ₃))

ω₅ = ^{(-V_b∗cos(θ₃) - ω₃∗b₂∗sin(θ₃))}⁄_{(b2∗sin(θ5))}

V_c2 = -(ω₃∗a₂∗cos(θ₃) - V_b∗sin(θ₃) + ω₅∗b₂∗cos(θ₅))