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A linearized model of a torque-controlled crane hoisting a load with a fixed rope length is
where
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CONTROL SYSTEMS ENGINEERING
- A robot joint is to be moved from initial position 15 degrees to final position of 45 degrees in 5 seconds using a 3rd order polynomial: q(t) = a0 + a1 *t + %3D a2*t^2 + a3*t^3. Assume that the initial and final velocities are zeros. Calculate the parameters a0, a1, a2, and a3 a0=0, a13D15, a2=D1.8, a3=0.6 a0=15, a1=0, a2=D45, a3=D0 a0=15, a1=0, a2=3.6, a3=-0.48 a0=15, a1=45, a2=D1.88, a3=-0.62arrow_forward5Find the lengh and divection for (uxv) X(vxu) 179 for the folloning @ u=2i+3j , v= -itj O u=2i-2j +4k,v= -i+j-2k ® u= irj-K, v= o O u= -gi -2j-4k, v= 2i+2j+k O u= i-tj+k, v= i+j+2karrow_forwardthe equivalent spring constant for ?below if the constant spring is 80 N/m k3 m3 k6 m1 m6 سرے کے نمبر کر کر کر کے k1 k4 m2 k2 k5 Non one of them O 480 O 540 O 840 Oarrow_forward
- 3. Find the response 0 of the rigid bar shown in Fig.3, using the convolution integral method for the following data: kj = k2 =5000 N/m, a=0.25m, b=0.5m, l=1.0m, M= 50 kg, m=10kg, Fo=500N. Compare the response when it is computed using the Laplace Transform Method. Uniform rigid bar, F(t) = Fe! mass m M Fig. 3arrow_forwardEquation of motion of a suspension system is given as: Mä(t) + Cx(t) + ax² (t) + bx(t) = F(t), where the spring force is given with a non-linear function as K(x) = ax²(t) + bx(t). %3D a. Find the linearized equation of motion of the system for the motion that it makes around steady state equilibrium point x, under the effect of constant F, force. b. Find the natural frequency and damping ratio of the linearized system. - c. Find the step response of the system ( Numerical values: a=2, b=5, M=1kg, C=3Ns/m, Fo=1N, xo=0.05marrow_forwardA mass of 2 kilograms is on a spring with spring constant k newtons per meter with no damping. Suppose the system is at rest and at time t = 0 the mass is kicked and starts traveling at 2 meters per second. How large does k have to be to so that the mass does not go further than 3 meters from the rest position? use 2nd order differential equations to solve (mechanical vibrations)arrow_forward
- Consider the following for a single-degree-of-freedom system with m = 1. X, k = 2.5, and c = 1.8. Here, the value of X indicating of the number of your Q1 (a) group. For example, if your group number is 15 gives X = 15, therefore the values of m = 1.15. If your group number is 9 gives X = 9, therefore the values of m = 1.9 Find; Natural frequency, Wn (ii) Linear frequency, fn (iii) Critical damping constant, c. (iv) Damping ratio, 3 (v) Damped frequency, Waarrow_forwardConsider two robot-manipulators:• A SCARA robot with joints displacement range q1,2 = −90◦...90◦ and q3 = 0..10cm and links lengths L1,2=10 cm.• A Cartesian robot with joint displacements’ range q1,2,3 = 0..10 cm.Which statement is correct?1) The Cartesian robot has a larger workspace.2) It is not possible to judge the workspace based on the information provided.3) Both robots have revolute joints.4) The SCARA robot has a larger workspace.arrow_forwardWERK the equivalent spring constant for below if the constant spring is 80 ?N/m k1 m3 k3 k6 m1 k4 m6 m2 k5 840 Non one of them 540 480 O k2arrow_forward
- 1. Equation of Motion 2. Find the response of the system, as the initial condition is (X, = 2 cm at the block). %3D Note: m= 1kg, Mlise 3 kg, c=50 N-s/m, k 200 N/m, and r= 10 cm. %3D and determine the response after 10 sec. 2r Activatearrow_forward4 QUESTION 20 The car bridge in Figure Q20 can be modelled as a damped-spring oscillator system with mass M = 10000 kg, spring coefficient k = 50000 N-m-1 and damping constant c = 50000 N-s-m-1. Cars cross the bridge in a periodic manner such that the bridge experiences a vertical force F (N) expressed by F = mg sin(10t) where m = 1136 kg is the average mass of passing cars, g = 9.81 m-s-2 is the gravitational acceleration and t (s) is the time. Determine the maximum force magnitude transmitted to the foundation (see Figure Q20) during the steady-state oscillatory response of the system. Provide only the numerical value (in Newtons) to zero decimal places and do not include the units in the answer box. E m M foundation Figure Q20: Vibrating car bridge.arrow_forwardParameters Mass 5kg A=2 B=7 C(m)=3 D(m)=4.583arrow_forward
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