1. A planar mechanism is designed to have two branches symmetrical to the centerline as shown. Explain briefly and clearly the main purpose of the redundant design, determine the mobility using Gruebler's equation, and then find the mechanical advantage at the position shown using a method of your choice. A Input Output B Note: The top and bottom branches are symmetric w.r.t. the centreline

Q: For the spring system shown in the accompanying figure, determine the displacement of each node. Start by identifying the size of the global matrix. Write down elemental stiffness matrices, and show the position of each elemental matrix in the global matrix. Apply the boundary conditions and loads. Solve the set of linear equations. Also, compute the reaction forces. k2 = 9 lb k1 = 20b in 20 lb k,=5 lb ww lb in kz = 5 lb in ks = 9 in lb k6 = 9 in 50 lb k4 = 20 lb kg = 20 b in in

A weight W= 120 kN is being supported by steel sections with force T, force F, andforce C. The coordinates of A, B, C, and D are given. Assume that E is the origin(0,0,0). Determine Forces T, F, and C. (Hint: Produce three equations fromequilibrium of force system)Note: The Forces T, F, and C must be computed accurately to design the proper sizes ofsteel sections in the subject “Steel Design.”

Determine the dof (mobility) of the following mechanisms

Solve the following with a free body diagram.

Block String Rod Disk Mech 3. As shown above, a uniform disk is mounted to an axle and is free to rotate without friction. A thin uniform rod is rigidly attached to the disk so that it will rotate with the disk. A block is attached to the end of the rod. Properties of the disk, rod, and block are as follows. Disk: Зт, radius R, moment of inertia about center ID = mR² mass = %3D Rod: m, length = 2R, moment of inertia about one end IR mR? mass = Block: mass = 2m The system is held in equilibrium with the rod at an angle 0, to the vertical, as shown above, by a horizontal string of negligible mass with one end attached to the disk and the other to a wall. Express your answers to the following in terms of m, R, 00, and g. (a) Determine the tension in the string.

PART 2: Determine whether the given mechanisms are Grashof's Chain, Non- Grashof's Chain or Transition chain using Grashof's criterion. Show your solution. 1. If: AB = 25 cm BC = 43 cm CD = 45 cm AD = 50 cm 2. If: AB = 1 ft BC = 1.8 ft CD = 2.4 ft AD = 3.5 ft D 3. If: AB = 6 in BC = 13.2 in CD = 21.1 in AD = 25.7 in

Load F In vehicle suspension design it is desirable to minimize the mass of all components. You have been asked to select a material and dimensions for a light spring to replace the steel leaf-spring of an existing truck suspension. The existing leaf-spring is a beam, shown schematically in the figure. The new spring must have the same length L and stiffness k as the existing one, and must deflect through a maximum safe displacement omax without failure. The width b and thickness t are free variables. Use the index you derive to rank the following candidate material for this application using data from Appendix A: High carbon steel, low alloy steel, titanium alloys and CFRP (carbon fiber reinforced epoxy). L HINT: Derive a material index for the selection of a material for this application. Note that this is a problem with two free variables: b and t; and there are two constraints, one on safe deflection Smax and the other on stiffness k. Use the two constraints to fix the values of…

Calculate the reaction forces on the bearing near the pulley and bearing at the far end of the shaft. Include a free body diagram and coordinates. Given the shaft length is 1 meter=  Mass=40Kg  Static load = 8600N Dynamic (running load) = 8400N   Some hints:1. This solution will require you to draw known forces and find unknown reactions in 2perpendicular planes and then add the horizontal and vertical reaction forces asvectors to find the reaction force (hypotenuse).2. Bearings are usually mounted as near as possible to the ends of the shaft withoutfouling the other machine elements. The bearing at the far shaft end can be mountedat the 1 meter point. The bearing at the pulley end should allow clearance to assemblethe pulley.3. Bearing reaction forces are typically simplified as a single point load through thebearing centre.

Pivot A constant density bar with mass m and length Lis held in place as shown. Use the usual x,y,z coordinates for the following questions. Celling Cable 12. Measuring from the pivot, in the space below draw the torque-pic for the weight force exerted on the bar. Be sure your torque-pic includes both an expression for r in terms of L and also the value for the angle between r and weight force. Bar 350 Length = L