Homework 1

Flexible links in robot arms are encountered in many industrial applications. Figures 1 and 2 show sketches of a laboratory model of such a link. The manipulator positions a load of mass M and length I at an angle q1. The link's flexible joint is modeled as a spring of stiffness k, and is driven by a de motor with a rotor that has an inertia J and friction B. The link's inertia is I. Flexible joint Mgl Motor and encoder Encoder Arm Fig. 1. Sketch of experimental hardware. Fig. 2. Model of single-link flexible-joint arm. (a) Find the equations of motions in time domain and Laplace domain. u(t) is the torque generated by the motor and g is the acceleration due to gravity. (assuming zero initial conditions)

Q/A circular disc of mass m and radius r is Qil 'connected to two springs. If it is free to roll onarough horizoutal surface without_slipping, use energy methad to calculat the System natural Trequency.

The EOM for the following 1-DOF gyroscope is: JÖ + BO + KO = Hw w is the angular velocity of the gyroscope about the input axis, is the angular position of the spin axis, H is the angular momentum stored in the spinning wheel, J is the mass moment of inertia of the wheel about the output axis, B is the viscous friction coefficient about the output axis, and K is the spring constant of the restraining spring attached to the spin axis. Determine the transfer function relating output to the input w. Case K spin axis output axis BOD Go Wheel spins at constant velocity input axis

dynamic of machinery question photo

R mo m The figure shows a pulley of mass mo that is modelled as a disk of radius R. It is fixed in position but free to rotate about an axle with a bearing at its centre. A massless inextensible strap passes over the disk and supports a mass m at one end and is restrained at the other by a spring of stiffness k. The disk does not move relative to the strap. Acceleration due to gravity, g, acts vertically downwards and has a value of 9.81 m/s?. The generalised coordinate z is the displacement of m from its equilibrium position.

Figure below shows a mass-spring model of the type used to design packaging systems and vehicle suspensions, for example. The springs exert a force that is proportional to their compression, and the proportionality constant is the spring constant k. The two side springs provide additional resistance if the weight W is too heavy for the center spring. When the weight W is gently placed, it moves through a distance x before coming to rest. From statics, the weight force must balance the spring forces at this new position. (if x=d) These relations can be used to generate the plot of x versus W. (a) The following values are given: k1=104 N/m; k2 = 1.5 *104 N/m; d =0.1 m. Create a function that computes the distance x, using the input parameter W; Then, test your function for the following two cases, using the values: W=500 N W=2000 N. (b) Create another script and use your function to plot x versus W for 0 < W < 3000 N for the values of k1, k2, and d given in part a.

* F2 # 3 E Problem 4. EOM Derivation Derive the equation of motion for the following system: We want to measure the spin rate w of the rotating shaft of a turbine. To do it we push a small mass m against the end of the shaft. The shaft makes friction contact with the drag cup mounted on the mass. The frictional torque is b (w). Assume that the rotational spring torque is ke and that the moment of inertia of mass m is J. J Rotating Shaft F3 @ $ 4 R b J, m Drag Cup F4 Q Search % 5 F5 T 0 Wall * A 6 F6 Y 2 * F7 & 7 PrtScn U F8 4 8 Home 6. F9 9 End F10 Po 0

Provide an FBD on this problem and please show complete answer.

For the problem related to Fundamental.6 sketches of the system showing: • the respective velocity and acceleration and the frame of reference considered • the forces acting on the system of considered, in other words, a free body diagram (FBD) are mandatory. Their absences will automatically make the problem false. The tractor is used to lift the 50-kg load B with the 27-m long rope, boom, and pulley system. The height h=4-m, SA=15m and sg=1.3m. SB B hm -SA If the tractor travels to the right with an acceleration of 3 m.s2. The maximum of tension of the allowable tension force in the rope is 3-kN. Determine the maximum of the allowable velocity of the tractor.

Theory of machine

The ABCD structure illustrated on the left is used to stop the rotational movement of an inertia wheel attached in O while having a cusion B in contact with the wheel. The static friction coefficient is 0,4 and the cinetic friction coefficient is 0,3. The couple M applied on the inertia wheel is 300N*m. The lineic weight of the ABC membrane is 200N/m. The effort of compression in the hydraulic cylinder CD is 3,50 kN and its weight is negligible. Determine: 0.6 m a) if the inertia wheel turns or not b) the efforts on the ABC part 1 m 30° B 60 mm A M 0.3 m

Mechanism design

Hi! I need answers in these three questions. Thank you!

Two masses A and B are 5kg and 2kg respectively rotating in a shaft. The corresponding radii of rotation are 0.2m and 0.3m respectively and the angle between the masses is 600. Find the position and magnitude of the balance mass required, if its radius of rotation is 200 mm using graphical method and also verify your answer with analytical method.

Problem 4: Use the principle of virtual work to determine the equation of motion for the system shown below. The rod is rigid and has a total mass of 1.5m. Assume small rotations. Rigid 1.5m L/2 L/2

Use image below and Draw a free-body diagram with the forces acting on the system.

4

Determine an equivalent lumped mass model for the crankpin.

8. Fig. 8 shows a simple aircraft landing gear, consisting of a spring and hydraulically loaded piston and cylinder D and the two pivoted links OB and CB. If the assembly is moving along the runway at a constant speed with the wheel supporting a stabilised constant load of 24 kN, calculate the total force that the pin at A supports. [Ans: 44.7 kN] Fig. 8 D 700 mm O B 30° 250 mm 250 mm

0.5 m, k = 500 N/m, and k = 40 N.m/rad, In the system shown, m = 10 kg, r = 0.3 m, Ko where ko is the radius of gyration of the pulley about point 0. There is no slippage between the cord and the pulley. Replace the system with an equivalent { a) torsional spring and mass moment of inertia at point 0, and b) translational mass and spring at point A. т, Ко kt А k m ww

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B r P F A UBC Engineering Your team is prototyping a simple braking system for your model car. The 3.4 kg wheel with a radius of r = rad 0.15 m is rotating at w = 18 - .A servo motor can apply a variable force F, which in its first two seconds of operation is equal to F = 10t N and afterwards is equivalent to a constant force of F = 20 N . If the coefficient of kinetic friction between the braking arm and the wheel is μ= 0.2, determine the time needed for the wheel to come to a full stop. The point of contact P between the wheel and the arm is a distance r = -0.2 + 0.26 ĵ m from point A. The force of the servo motor is applied at exactly half of the horizontal distance to A from the point of contact. Assume the wheel can be treated as a disk and that the braking arm is massless. t =

01: A 105cm Rod is suspended on a wall with a 5N force pulling upwards, 110 degrees away from the horizontal axis and 5cm from a 50kgm hanging object. Find the location of the C.G. away from the wall. Neglect the Mass of the rod and consider it a rigid body. Assume SSLC. 02: Considering a CCW movement is Positive, what is the total value of the Negative Moments at the point with the 50kgm object? Please answer in four decimal places, in Nm. 03: What is the value of C.G. away from the wall? (in meters, two decimal places)

Questions A and B

Stirrer A, B and C with a specifications of m = 5 kg, m³ = 3 kg, mc = 4 kg and r = 1 m, rв = 2 m, rc = 2 m respectively to be fix at rotating shaft of a machine. Using a graphical method with a scale of 5 kgm = 50 mm, suggest the stirrer orientation measuring from positive x axis to achieve static balance mode.

Please solve with step and explaining, thank u

Consider the system shown at right. Find an equation of motion for the block with mass m,. Assume that the small wheel has negligible mass moment of inertia and that the larger one has a radius R and a mass moment of inertia I (measured respect to its axis of rotation). Note that there is a friction between the block with m2 mass m2 and the plane. The dynamic friction coefficient is equal to µa. m1 Md