Synthesis and Dynamic Simulation of Mechanism | Brunel assignment | Dr Yohan Noh
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Question 1:
Given a mechanism with the link lengths L1x = 0.62 m, L1y = 0.19 m, L2 = 0. 325
m, L3 = 0.16 m, and L4 = 0. 18 m, L5x = 0.1 m, L5y = 0.16 m, L6 = 0.35 m, lg2 =
0.17115 m, lg3 = 0.09026, lg4 = 0.09m, lg6 = 0.175m, I2 = 0.089191665 kg·m2
, I3 =
0.01389689, kg·m2
I4 = 0.01435385 kg·m2 , and I6 = 0.130437 kg·m2
, find the
values for θ3, θ4, θ5, θ6, ω3, ω4, ω5, ω6, α3, α4, α5, and α6 as shown in Figures 1,
2, and 3 for the open circuit of the linkage assuming θ2 = 54.12°, ω2 = -25
rad/sec, and α2 = -15 rad/sec2
.
The mass density is ρ=30000kg/m3
, the link thickness T is 0.02 m, the joint
shaft and hole diameter is 0.025 m, and the link radius is 0.02 m.
There is an external torque (τ N·m) on one of the links, applied at the centre of
mass on one of the links, and at the same time an external force of Fp acts on
link 5, applied at point p and lf [m] away from point A. Please note that
depending on your student ID, you will get a different Fp and lf values (see the
additional document).
Find F12, F32, F62, F43, F54, F56, and F15 at the joints and the driving torque τ12
needed to maintain motion with the given angular velocity ω2 = 25 rad/sec and
acceleration α2 = 15 rad/sec2
for this instantaneous position of the link (Figures
1 to 3).
1) Find the values of θ3, θ4, θ5, θ6, ω3, ω4, ω5, ω6, α3, α4, α5, and α6
2) Find the centre of mass values lg5 of link 5.
3) Find the mass moment of inertia (kg·m2
) about the centre of mass of link
5.
4) Find the values of Ag2 Ag3 Ag4 Ag5 Ag6 of links 2, 3, 4, 5, and 6 (see Figure
3).
5) Find the force and moment equations for dynamic force analysis on links
2, 3, 4, 5, and 6, and cast the equations in the matrix form, and find the
values for F12 (F12x and F12y), F32 (F32x and F32y), F62 (F62x and F62y), F43 (F43x
and F43y), F54 (F54x and F54y), F56 (F56x and F56y), and F15 (F15x and F15y) at the
joints and the driving torque τ12 needed to maintain motion with the
given angular velocity and acceleration of ω2 = 25 rad/sec and α2 =15
rad/sec2
, respectively, for this instantaneous position of the link
Question 2:
For the robot mechanism described in Question 1, simulate it for the case in which the motion begins with a given crank angle θ2[rad] (find it in the figure), a given crank angular velocity ω2 = 0 rad/s and a given angular acceleration α2= 0.45 rad/s2in link 2.
The matrix equation (matrix form in Question 1) is solved using a MATLAB
User-defined function that will take all of the integrator outputs as input
arguments (Figure 1).
1) Plot the values of θ2, θ3, and θ4 for the first 2 seconds.
2) Plot the values of ω2, ω3, and ω4 for the first 2 seconds.
3) Plot the values of α2, α3, and α4 for the first 2 seconds.
4) Plot the values of AA AB, and AC at points A, B, and C for the first 2
seconds.
5) Plot the values of Ag2 Ag3, and Ag4 (at the centre of mass) of links 2, 3, and
4 for the first 2 seconds.
6) Plot F12 (F12x and F12y), F32 (F32x and F32y), F43 (F43x and F43y), and F14 (F14x
and F14y), at the joints and the driving torque τ2 needed to maintain
motion for the first 2 seconds.
7) Plot the coupler curve (plot x positions versus y positions) at the point of the centre of mass at Point P for the first 2 seconds.
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