The matrix will be written in the form: A= is the multiplying variable of the instantaneous geometry of the mechanism, B= is the multiplying variable defines the velocitys and acceleration links. Figure 17 shows the variation of angular velocity for the 21. http://mathworld.wolfram.com/Circle-CircleIntersection.html.
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function output = FourBarLinkageForHSBMtool_01(v) % 4-bar linkage for HSBM tool % clear; % v.bcDia = 6000; % v.hsbmPins = [2500, -500; 2500, 500]; % v.arms = [300, 600 300]; % v.ang = 20; % angle of upper component. The joints parameters featured for each link have the appropriate features such as the revolute and the slider. It's in one of the comments. ang = atan2(input(2,2)-input(3,2),input(2,1)-input(3,1)); % angle of coupler point2(i,:) = [0,150]*[cos(ang), sin(ang); -sin(ang), cos(ang)]+point(i,:); % offset point of the coupler, input = [input(1,:); % add center point and offset to the mech. A constrained rigid body system, in which one of the bodies is in the frame is referred to as a mechanism. Figure 15 shows the four-bar linked mechanism assembled and an emotion simulation. Press question mark to learn the rest of the keyboard shortcuts. Before carrying out the simulation, a mathematical model of the system needs to be developed. I see that the center vertical bar cannot pass through (it strikes) the top pivot; so what's going on when this bar passes through/over the bottom pivot? y[gC(C(9,SrY #;=Oo92E&0DXM Fxywxpyx0ub$J)]E#jeBH9Zs2=S4Dp This explains the fluctuation of the peaks shown for the torque above. It is seen that both angles are positive, as they rotate along the excesses in an anticlockwise direction.
It is shown that the mega one begins a lower place than omega one at around 1 rad/sec, with omega two starting above 10 rad/sec. This project consisted of using both MATLAB and Siemens NX to carry out simulations and analysis of mechanism systems.
I think that's why the blue dots show some odd behavior at the bottom. endobj
The simpler of the two methods was the modelling method using MATLAB. To create the two-bar link manipulator, assembly components with the appropriate parameters were modelled. <<
An increase in velocity is noticed in the second angle when in comparison to the first this is due to rapid acceleration. endobj
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% plot3(d.armLow(:,1), d.armLow(:,2),zeros(length(d.armLow),1),'-.r') % plot3(d.armUp(:,1), d.armUp(:,2),zeros(length(d.armLow),1),'-.k') % plot3(d.coupler(:,1), d.coupler(:,2),zeros(length(d.coupler),1),'-.b') % plot3(d.bar(:,1), d.bar(:,2),zeros(length(d.bar),1),'--ro'), axis equal xlim([1.5 3.5]*1e3) % ylim([-.75 .75]*1e3) view(0,90) end. After creating the parts in NX and assembling it to create both the two bar and the four-bar mechanisms, setting up the joint parameters was fairly simple, but problems occurred during the orientation of the assembly during the motion simulation process this resulted in graphs that was similar compared to the MATLAB counterpart but was not correct. Figure 24-Figure 26 show a close resemblance to Figure 19-Figure 21, but the magnitudes shifted slightly indicating an orientation or fault during the NX modelling process. stream
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Matrices can now be used to solve the dynamic equations used above. n.as orgAngle = atan2((y2-y1),(x2-x1)); % rotate X2 by -OrgAngle-> you only need centDist for calc, add this later % to result. This project consisted of using both MATLAB and Siemens NX to carry out simulations and analysis of mechanism systems.
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F!JT1^w By squaring and adding up both sides of the equations, the following equations are obtained: For MATLAB to be able to produce results the XY position of each link needs to be calculated. %
A counter-clockwise direction is taken in a horizontal axis to calculate the angles. <>>>
point(i,:) = mean(input(2:3,:)); % center point of coulpler. Theta two, on the other hand, starts in a positive position and begins to increase to points beyond 150 degrees steadily. The first angular velocity has lower peak point in the second angular velocity, but the second angular velocity sees a sharp decrease of this peak is reached when compared to the first angular velocity. %
points. 11 0 obj
input(2,:); point(i,:); point2(i,:); point(i,:); input(3,:); input(4,:)]; % xlim([1.9 3.2]*1e3) xlim([-1 1]*6e2) ylim([-1 1]*8e2) grid on % axis equal % view(0,90) drawnow pause(0.01). I know there is something wrong with the sharp angle at the top. endobj
X= The sum of the multiplying variables A and B and where the plot for the MATLAB results will be obtained from. To create the four bar-linked mechanism for links part models shown in Figure 11-Figure 14 had to be created in NX which would then be assembled into the mechanism. <>>>
Link AD simulated to be the ground and is set in an always stationary position. 1 0 obj
Link AB: To analyse the angular velocity to the derivative of Equation 3 and Equation 4 are carried out, giving the following: To calculate the angular acceleration, the derivative of the equations above in the velocity analysis can be taken to obtain: The force conditions on points A, B, C and D need to be calculated to obtain the centre of mass acceleration: The forces, as well as the torque acting in both the XY direction in links AB, BC, and CD need to be calculated individually to carry out a dynamic analysis. Thanks. The lower arm is just rotating and then I find the intersection of two circles with a radius of the upper arm and the coupling arm. Please post your code. |_IEJv28;9;2utv;&caQ{|r9;k M81)19>j{nzCys"'*MOrBtV)l\$wc24]"XbDB&oymNNLRedAr-Dx;)>;UB'Tq0js]eL$`U!kF?a~~Wn_0 wf# 5Cqj83IqCC[I%rA1_#y_,BR5~d_ Vb,+^Qh{:[66&d48.>j4zN(C
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clear clf set(gcf,'Color','w') v.arms = [410 1000 420]; v.bcDia = 6000; v.hsbmPins = [0 -500; 0 500]; v.resol = 50; filename = '4bar_01.gif'; for i = 1:140 % v.ang = -.4+i/20 v.ang = i/20; input = FourBarLinkageForHSBMtool_01(v); % this gives the 4 point for the mechanish. We use cookies on our websites for a number of purposes, including analytics and performance, functionality and advertising. The parameters given of the four-bar link system are the following: Table 1: Tables of parameters for the four-bar linked mechanism. 2 0 obj
Of the two intersections of these circles it just picks one. The same can be said for joints C and D. Figure 22 above shows the variation when a torque is applied to joints A and B(see Figure 8).At each cycle of the mechanism there is an increase in the torque of the motor and the angular velocity is constant. MATLAB software will be used to create a simulation of both these link bar mechanisms, with defining variables, such as the velocity, length, mass and inertia. For this project the simulation and analysis of a hypathtical two-bar linked planar manipulator which welds a structure in a production line was carried out.
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Before carrying out the simulation, a mathematical model of the system needs to be developed. This commit does not belong to any branch on this repository, and may belong to a fork outside of the repository. The two-bar link planar manipulator shown in Figure 1, consists of link OA, which is fixated to the point of and to the link AB at point A. 1 0 obj
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It is apparent that Figure 18 and Figure 19 a very similar in creating perhaps most joints having the same magnitude while moving with the constant velocity. For theoretical calculations, MATLAB is a popular software when it comes to the analysis of experimental data. Figure 18: Polar load diagram for joint A, Figure 21: Polar load diagram for joint D. Figure 18-Figure 21 shows the polar loads of joints A, B, C and D and is the result of the dynamic analysis of all the forces. You signed in with another tab or window.
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I would love to have this. %PDF-1.5
The four-bar link mechanism shown Figure 7 in consists of three links, link AB, BC, CD and DA which represents the ground. >>
Solving for both 11 and 11 gives: By squaring and adding up both sides of the equations the mechanisms position can be found: The angular velocity can now be calculated using both Equation 1 and Equation 2 from above differentiating with respect to time: The two-link bar manipulator was modelled on Siemens NX software in order to carry out a motion simulation of the arm. <>
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Also a four-bar link planar mechanism thats would be driven by an electric motor was also simulated analyed. <>
As the link moves energy is stored in the link and when the energy generated from the torque of the motor is zero, the energy stored in the link returns to the motor and vice versa. <>
Figure 26:Polar load diagram results for joint C in NX, Figure 27:Polar load diagram results for joint D in NX.
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Figure 24: Polar load diagram results for joint A in NX, Figure 25:Polar load diagram results for joint B in NX. When considering a constrained rigid body system, the degrees of freedom of that mechanism is important. stream
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Figure 15: Completed assembly in motion simulation, Figure 16: Variation of link orientations. A${Y~TWdL/%=5,q?ne t{2?BS6tg. S"D3yh2NgC)C2}S5AQp@-hAH$RI4T8
eFq:,"g Figure 23 shows the variation of the link angular velocity, and when compared to the results produced from the MATLAB plot, the results are the same except the that the angular velocity values are positive due to NX not providing negative values. if r1>r2 xt = centDist-(centDist2-r12+r22)/(2*centDist); else xt = (centDist2-r22+r12)/(2*centDist); end yt = 0; else if r1>r2 xt = centDist-(centDist2-r12+r22)/(2*centDist); yt = (sqrt(r12-xt2)); else xt = (centDist2-r22+r12)/(2*centDist); yt = (sqrt(r12-xt2)); transformOutput = [xt yt; xt -yt][cos(orgAngle) sin(orgAngle); -sin(orgAngle) cos(orgAngle)]; Output = [transformOutput(:,1) + x1, transformOutput(:,2) + y1]; if yt == 0; Output = Output(1,:); end % end % Output % plot % v.resol = 100; % clf % plot(x1,y1,'or'); hold on % plot(x2,y2,'ok') % plot(x21,y21,'ok') % plot(xt,yt,'+b','markersize',20) % plot(xt,-yt,'+b','markersize',20) % clear c1 c2 % for i = 1:v.resol % c1(i,:) = r1[cos(i2pi/v.resol) sin(i2pi/v.resol)]'+[x1 y1]'; % c2(i,:) = r2*[cos(i2pi/v.resol) sin(i2pi/v.resol)]'+[x2 y2]'; % c2(i,:) = r2*[cos(i2pi/v.resol) sin(i2pi/v.resol)]'+[x21 y21]'; % end % c1(end+1,:) = c1(1,:); % plot(c1(:,1), c1(:,2), 'r') % plot(c2(:,1), c2(:,2), 'k') % % axis equal % % grid minor % grid on % % for i = 1:size(Output,1) % plot(Output(i,1), Output(i,2),'+b','markersize',20) End, Press J to jump to the feed. To ensure that point B travels in a straight-line path in the XY coordinates, from (0.3m,0.0m) to (0.0m,0.3m) with a constant velocity of 2 m/s, the angles 1 and 2 will be controlled. function Output = circcirc(x1,y1,r1,x2,y2,r2) % intersection of two circles; 3 cases, % 0 intersection, 1 intersection/toutching, 2 intersections (normally) % info on circ1(x1,y1,r1) and circ2(x2,y2,r2) % http://mathworld.wolfram.com/Circle-CircleIntersection.html % clear % x1=6; y1=0; r1=5; % x2=0; y2=0; r2=2; centDist = sqrt((x1-x2)2+(y1-y2)2); % remove X1 from both X1 and X2. endobj
The code is not very refined. 3 0 obj
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%generate points circle of the brake disk % v.resol = 50; for i = 1:v.resol d.bd(i,:) = [v.bcDia/2cos(i/v.resol2pi), v.bcDia/2sin(i/v.resol2pi)]; % circle for the brake disk % d.armLow(i,:) = [v.arms(3)cos(i/v.resol2pi), % v.arms(3)sin(i/v.resol2pi)]; % d.armUp(i,:) = [v.arms(1)cos(i/v.resol2pi), % v.arms(1)sin(i/v.resol2pi)]; % d.coupler(i,:) = v.arms(2)[cos(i/v.resol2pi) sin(i/v.resol2*pi)]; end % d.coupler(end+1,:) = d.coupler(1,:); % d.armLow(end+1,:) = d.armLow(1,:); % d.armLow= [v.hsbmPins(1)+ d.armLow(:,1) v.hsbmPins(3)+ d.armLow(:,2)]; % d.armUp(end+1,:) = d.armUp(1,:); % d.armUp = [v.hsbmPins(2)+ d.armUp(:,1) v.hsbmPins(4)+ d.armUp(:,2)]; d.bar(1,:) = v.hsbmPins(1,:); d.bar(2,:) = d.bar(1,:)+v.arms(1)*[cosd(v.ang), sind(v.ang)]; % d.coupler= [d.bar(2,1)+d.coupler(:,1) d.bar(2,2)+d.coupler(:,2)]; d.bar(1,:) = v.hsbmPins(1,:); d.bar(2,:) = d.bar(1,:)+v.arms(1)*[cos(v.ang), sin(v.ang)]; d.bar(4,:) = v.hsbmPins(2,:); % intersection of circles; d.circIntersection = circcirc(d.bar(4,1),d.bar(4,2),v.arms(1), d.bar(2,1),d.bar(2,2),v.arms(2)); d.bar(3,:) = d.circIntersection(1,:); output = d.bar; % plot the figure. <>
To conclude both methods (MATLAB and NX) were valuable for carrying out the dynamics and kinematic analysis of a mechanism. Theta one begins above -50 degrees and increases to an angle of approximately 50 degrees indicating a continuous upward direction. I hope I included all the sub-functions. The mechanisms will also be modelled in Siemens NX, which a motion simulation will then be carried out to produce graphical results which will be compared against results produced in MATLAB. Link AB is the moving force and the mechanism and rotates counterclockwise at an angular velocity of 100 rads/s. The parameters given of the two-bar link system are the following: A mathematical analysis will be performed to obtain equations that describe the system. Figure 16 above shows variation of link orientation with the angles theta 1 and theta 2. x\[s6~OU-M /S)W:4[ci{@
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sum of radius is smaller than distance between X1 and X2 if centDist > (r1+r2) Output = [0 0; 0 0]; % no intersection elseif centDist == (r1+r2) % toutching! xZmo6 bNi( Link AB is driven by a motor with the torque force Tm starting the movement in the mechanism, CD then carries the load torque Tl. Design-and-Analysis-of-2-and-4-bar-mechanisms, Design and Analysis of 2 and 4 bar mechanisms, The completed assembly in a motion simulation, MATLAB results for Two bar link mechanism, MATLAB results for Four-bar link mechanism, NX simulation results for Two bar link mechanism, NX simulation results for Four-bar link mechanism. % clf % hold on % plot3(d.bd(:,1), d.bd(:,2), zeros(length(d.bd),1) ,'-.') This is cool.