Solution K2-51 (Figure K2.5 condition 1 S.M. Targ 1989)

The solution to problem K2-51 (Figure K2.5 condition 1 S.M. Targ 1989) represents a mechanism consisting of three stepped wheels 1-3. The wheels are engaged or connected by a belt drive, a toothed rack 4 and a weight 5 tied to the end of a thread wound around one of the wheels (Fig. K2.0 - K2.9, Table K2). The radii of the wheel steps are respectively equal: 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 of the wheels, points A, B and C are located. The table shows the laws of motion or the laws of change 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 change angular velocity of the wheel 2, v5(t) - the law of change in the speed of the load 5, etc. (everywhere φ is expressed in radians, s - in centimeters, t - in seconds). 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.).

Solution K2-51 (Figure K2.5 condition 1 S.M. Targ 1989)

Solution of problem K2-51, presented in Figure K2.5, condition 1 S.M. Targ 1989 is a digital product available for purchase in our digital product store.

This solution contains a detailed description of a mechanism consisting of three stepped wheels 1-3, meshed or connected by a belt drive, a gear rack 4 and a weight 5 tied to the end of a thread wound around one of the wheels. The radii of the wheel steps are respectively equal: 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 attached to the solution indicates the laws of motion or the laws of change in the speed of the driving link of the mechanism, which makes it possible to determine at the time t1 = 2 s the velocities indicated in the “Find” columns (v - linear, ω - angular) and accelerations (a - linear , ε - angular) of the corresponding points or bodies (v5 - speed of load 5, etc.).

Using this solution, you can easily and accurately determine the speeds and accelerations of various elements of the mechanism at a given point in time, which will allow you to solve mechanical problems with high accuracy.

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The K2-51 solution is a mechanism that consists of three stepped wheels and a gear rack connected by a belt drive. The wheels are meshed and driven by a weight tied to the end of a thread wound around one of the wheels. The radii of the wheel steps are different and 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. Points A, B and C are located on the wheel rims.

For the mechanism, the laws of motion or changes in the speed of the driving link are indicated in the “Given” column of the table. For example, 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 changing the angular velocity of wheel 2, v5(t) is the law of changing the speed of load 5, etc. At the moment of time t1 = 2 s, determine the velocities (v - linear, ω - angular) and accelerations (a - linear, ε - angular) of the corresponding points or bodies (v5 - speed of load 5, etc.) indicated in the table in the "Find" columns. d.).

Thus, Solution K2-51 is a mechanism that allows you to determine the speeds and accelerations of various points at time t1, based on the laws of motion or changes in the speed of the leading link.

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