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Assume a crankshaft is at determined instantons angle and position as shown in Figure.4, 300 грm 200 mm 100 mm 600 Figure.4: Instantons positions of piston in crankshaft mechanism By making use of trigonometric methodology, you are required to find the following parameters of the planar mechanisms: 1. Find the tangential velocity (V¼)o 2. Construct diagrams to show, the rotational motion (tangential velocity vector OA) of link OA, combined rotational and translational motions (relative tangential velocity AB) of link AB, and the pure translational motion of Piston B. 3. On the previous velocity vector diagram, use sine and cosine rules to find the necessary angles and vector magnitudes. 4. Find the tangential velocity (Vg)a and then find the angular velocity of link AB, waB 5. Find the translation velocity of the piston, (Vg)o

Assume a crankshaft is at determined instantons angle and position as shown in Figure.4, 300 грm 200 mm 100 mm 600 Figure.4: Instantons positions of piston in crankshaft mechanism By making use of trigonometric methodology, you are required to find the following parameters of the planar mechanisms: 1. Find the tangential velocity (V¼)o 2. Construct diagrams to show, the rotational motion (tangential velocity vector OA) of link OA, combined rotational and translational motions (relative tangential velocity AB) of link AB, and the pure translational motion of Piston B. 3. On the previous velocity vector diagram, use sine and cosine rules to find the necessary angles and vector magnitudes. 4. Find the tangential velocity (Vg)a and then find the angular velocity of link AB, waB 5. Find the translation velocity of the piston, (Vg)o

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Problem 3: Crankshaft mechanism is one of the most important mechanical system used to convert translational motion or reciprocating motion to rotational motion and vice versa. It is widely used in cars' engines and hydraulic pumps. Your role in car's engine manufacturing company is to analyze the displacement, velocity and acceleration diagrams for crankshaft planer mechanism to later find the forces of the links to avoid overloading the system. Your manger asked you the provide detailed analysis of the crankshaft planar mechanism shown in Figure.3. Part.1: -140 mm 60 mm Crank Connecting Rod x(t) V(t) a(t) F(t) (OB Piston x(t) Reference Figure.3: Crankshaft planar mechanism for a car 'engine. If the zero-position x=0 at the extreme right as shown in Figure.3, perform the following tasks: 1. Derive a mathematical relation for displacement, velocity and acceleration x(t), v(t) and a(t) of the piston B. 2. Derive a mathematical relation for force F(t) on the piston B by making use of the a(t). 3. Plot all the relations you have found using MatLab, note that you should end up with plots like Figure.4. 4. Find the acceleration and force of the Piston B when the crank rotational speed is 30 rpm.
Transcribed Image Text:Problem 3: Crankshaft mechanism is one of the most important mechanical system used to convert translational motion or reciprocating motion to rotational motion and vice versa. It is widely used in cars' engines and hydraulic pumps. Your role in car's engine manufacturing company is to analyze the displacement, velocity and acceleration diagrams for crankshaft planer mechanism to later find the forces of the links to avoid overloading the system. Your manger asked you the provide detailed analysis of the crankshaft planar mechanism shown in Figure.3. Part.1: -140 mm 60 mm Crank Connecting Rod x(t) V(t) a(t) F(t) (OB Piston x(t) Reference Figure.3: Crankshaft planar mechanism for a car 'engine. If the zero-position x=0 at the extreme right as shown in Figure.3, perform the following tasks: 1. Derive a mathematical relation for displacement, velocity and acceleration x(t), v(t) and a(t) of the piston B. 2. Derive a mathematical relation for force F(t) on the piston B by making use of the a(t). 3. Plot all the relations you have found using MatLab, note that you should end up with plots like Figure.4. 4. Find the acceleration and force of the Piston B when the crank rotational speed is 30 rpm.
Part.2: Assume a crankshaft is at determined instantons angle and position as shown in Figure.4, ► 3000 rpm 200 mm 100 mm 600 B Figure.4: Instantons positions of piston in crankshaft mechanism By making use of trigonometric methodology, you are required to find the following parameters of the planar mechanisms: 1. Find the tangential velocity (Va)o 2. Construct diagrams to show, the rotational motion (tangential velocity vector OA) of link OA, combined rotational and translational motions (relative tangential velocity AB) of link AB, and the pure translational motion of Piston B. 3. On the previous velocity vector diagram, use sine and cosine rules to find the necessary angles and vector magnitudes. 4. Find the tangential velocity (Vg)a and then find the angular velocity of link AB, wAB 5. Find the translation velocity of the piston, (Vg),
Transcribed Image Text:Part.2: Assume a crankshaft is at determined instantons angle and position as shown in Figure.4, ► 3000 rpm 200 mm 100 mm 600 B Figure.4: Instantons positions of piston in crankshaft mechanism By making use of trigonometric methodology, you are required to find the following parameters of the planar mechanisms: 1. Find the tangential velocity (Va)o 2. Construct diagrams to show, the rotational motion (tangential velocity vector OA) of link OA, combined rotational and translational motions (relative tangential velocity AB) of link AB, and the pure translational motion of Piston B. 3. On the previous velocity vector diagram, use sine and cosine rules to find the necessary angles and vector magnitudes. 4. Find the tangential velocity (Vg)a and then find the angular velocity of link AB, wAB 5. Find the translation velocity of the piston, (Vg),
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