Solution K2-88 (Figure K2.8 condition 8 S.M. Targ 1989)

The solution to problem K2-88 (from condition 8 on page 76 of the textbook by S.M. Targ, published in 1989) is based on the use of stepped wheels 1-3, which interact with each other using a belt drive and a gear rack 4. A load 5 is attached to the end of the thread wound around one of the wheels. Figures K2.0 - K2.9 and table K2 contain information about the mechanism. The wheels have radii r1=2 cm, R1=4 cm, r2=6 cm, R2=8 cm, r3=12 cm and R3=16 cm. Points A, B and C are located on the wheel rims. In the “Given” column of the table it is indicated how the speed of the driving link of the mechanism changes (φ1(t) - law of wheel rotation 1, s2(f) - law of rack motion 4, ω2(t) - law of change in angular speed of wheel 2, v5(t) - law of change in load speed 5, etc.). In all cases, φ is expressed in radians, s in centimeters, and t in seconds. The positive direction for φ and ω is counterclockwise, for s4, s5, v4 and v5 - down. It is necessary to determine the velocities (v - linear, ω - angular) and accelerations (a - linear, ε - angular) of the corresponding points or bodies at the time t1=2 s, indicated in the “Find” columns of the table.

Here we present a unique digital solution to the K2-88 problem, based on a mechanism with stepped wheels, a belt drive and a rack and pinion. The solution includes a detailed description of the mechanism, radii of the wheel steps and location points on the wheel rims. The table shows the laws of motion and changes in speed for all elements of the mechanism, and also indicates the positive direction for speeds and angular velocities in accordance with their movement. At time t1=2 s, the table provides information about the velocities and accelerations of the corresponding points or bodies. Solution K2-88 is based on materials from the textbook by S.M. Targa 1989 and is a valuable resource for students and professionals in the field of mechanics. Beautiful design in HTML format makes viewing and reading the solution more convenient and attractive.

Solution K2-88 is a mechanics problem that describes the movement of a mechanism with stepped wheels, a belt drive and a rack. The mechanism consists of three wheels meshed or connected by a belt drive, a gear rack and a weight tied to the end of a thread wound around one of the wheels. The radii of the wheel steps are equal respectively: for wheel 1 – r1 = 2 cm, R1 = 4 cm, for wheel 2 – r2 = 6 cm, R2 = 8 cm, for wheel 3 – r3 – 12 cm, R3 = 16 cm. On rims the wheels are located at points A, B and C.

The table shows the laws of motion and changes in speed for all elements of the mechanism, and also indicates the positive direction for speeds and angular velocities in accordance with their movement. At time t1 = 2 s, the table provides information about the velocities and accelerations of the corresponding points or bodies.

To solve the problem, it is necessary to determine the velocities (v - linear, ω - angular) and accelerations (a - linear, ε - angular) of the corresponding points or bodies at the time t1 = 2 s, indicated in the “Find” columns of the table.

The K2-88 solution is a unique digital solution to the K2-88 problem, based on materials from the textbook by S.M. Targa 1989. It is a valuable resource for mechanical engineering students and professionals and is presented in an attractive HTML format for easy viewing and reading.

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The K2-88 solution is a mechanism consisting of three stepped wheels, a gear rack and a weight tied to the end of a thread wound around one of the wheels. The radii of the wheel steps are different: for wheel 1 - r1 = 2 cm, R1 = 4 cm, for wheel 2 - r2 = 6 cm, R2 = 8 cm, for wheel 3 - r3 = 12 cm, R3 = 16 cm. On the wheel rims points A, B and C are located.

The table shows the laws of motion or changes in the speed of the driving link of the mechanism, where φ1(t) is the law of rotation of wheel 1, s2(f) is the law of motion of the rack 4, ω2(t) is the law of changes in the angular velocity of wheel 2, v5(t) - law of change in speed of load 5, etc. The positive direction for φ and ω is counterclockwise, for s4, s5 and v4, v5 - down.

It is necessary to determine at the moment of time t1 = 2 s the velocities (v - linear, ω - angular) and accelerations (a - linear, ε - angular) of the corresponding points or bodies indicated in the table in the "Find" columns (v5 - speed of load 5, etc.) .d.).

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