A) Prove that the tool Jacobian matrix of the 3R Planar robot (shown in the figure) is given by the matrix below: -LS-LS-LS123 - L₁₂S12-L3 123-35123] V(a)=49+L2 + L3G23 1 L₂G12 + L3G123 1 B) Find the singular configuration of the robot. ჩვ. L3C123 1 02 L2
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- Please find the question attached. I don’t understand how to integrate when finding the pathline.You are the mechatronics engineer of a manufacturing plant. You decide to perform an analysis on a robot arm of the assembly line with the objective of optimizing its performance. After taking several readings of the speed of the arm’s end effector, you approximate its velocity to the function given below. v(t) = -t4 + 5t3 - 7t2 + 3t + 0.22 0 =< t =< 3 where the velocity is in ms-1 d) Knowing that the distance travelled by an object is the area under its velocity-time graph, determine the distance travelled by the end effector on the interval 0 =< t =< 1 by using the mid-ordinate rule. Simpson’s rule correct to 3 decimal places using four intervals. e) Calculate the same distance as in (d) above by using the appropriate definite integral. f) Compare the distances you calculated in (d) and (e) above and comment on the accuracy of the two methods you used in (d)Derive the governing differential equation for each system with the chosen generalized coordinate. SEE THE IMAGE BELOW Answers: 1. GDE: (5/2) mẍ + (5/4) kx = 0 2. GDE: (7/48) mL² ϴ [note: theta symbol has two dots above) + (3/8) cL² ϴ [ note: theta symbol has one dot above] + 5 kL² ϴ = 0
- A weight is attached to a spring suspended from a beam. At time t = 0, it is pulled down to a point 8 cm above the ground and released. After that, it bounces up and down between its minimum height of 8 cm and a maximum height of 24 cm, and its height h(t) is a sinusoidal function of time t. It first reaches a maximum height 1.4 seconds after starting. (a) Follow the procedure outlined in this section to sketch a rough graph of h(t). Draw at least two complete cycles of the oscillation, indicating where the maxima and minima occur. (b) What are the mean, amplitude, phase shift and period for this function? (Use a phase shift with an absolute value less than the period.) mean 16 amplitude 8 phase shift ___ period 2.8 (c) Give four different possible values for the phase shift. (Enter your answers as a comma-separated list.) _______ (d) Write down a formula for the function h(t) in standard sinusoidal form; i.e. as in the…sole using laplace transforms Do not answer in image formatIdentify the three rectilinear kinematic equations and their limitations.
- Please just question C. Instead of solving part C how it says can you solve by using k1=k2=1N/m m1=m2=1kg, l=1m, g=10m/s^2, use [X,wn2]=eig(K,M) to find the natural frequencies for both sets of coordinates. Thank youTell whether the following functions are linearly dependent or linearly independent using the Wronskian." Centroids " from the Book Engineering Mechanics Statics and Dynamics by Ferdinand Singer. I think the solution is like the one in the second picture, i just cannot get the right answer in the answer key given please help me thankyou! I think the one that is in the answer key was the Xbar (X̅) and Ybar ( ȳ ).
- Somewhere DEEP BELOW THE EARTH's surface, at an UNKNOWN displacement from the Earth's center, a particle of mass m is dangled from a long string, length L; the particle oscillates along a small arc according to the differential equation d^2x/dt^2=-(pi^2/36)x. Here x refers to an angular displacement measured from the vertical and t refers to time. The particle's mass is given by m=3kg. The length of the string is given by L=5 meters. Whenever the particle arrives at a location of x=(pi/12) radians from the vertical, the particle has no instantaneous speed. On both sides of the vertical, that is, x=(pi/12) radians is repeatedly observed to be a 'turning point' for the particle's periodic motion. 1. Draw a clear FREE-BODY diagram of this particle at some arbitrary point during oscillation, making sure to label variables and constants described above. 2. Approximating to three significant digits if necessary, what is the angular frequency of this oscillator on a string? 3. Approximating…Solve the inverse kinematic problem for the following 6 DOF robot, using the method ofkinematic decouplingif it is known that its Denavit-Hartenberg parameters are as shown in the table inthe tableNo.16: a.) Describe the Bicubic patches with mathematical functions. b.) Enumerate various desired modeling facilities required for Industries.