Scotch Yoke mechanism - Displacement. velocity and acceleration analysis - Hand written notes

 Scotch Yoke mechanism - Displacement. velocity and acceleration analysis - Hand written notes

In this article for a variation of Scotch Yoke Mechanism displacement, velocity and acceleration equations derived.

Watch it on YouTube: https://youtu.be/guce8wESqTE

In the below picture shown is a variation of Scotch Yoke Mechanism, where length of the crank is R, and angle between sliding block and plunger/vertical axis is beta.

In the below pictures, described how to derive equation to find displacement of the plunger (x) in terms of crank length R, crank angle theta and sliding block angle alpha.

To find the velocity of plunger (V), differentiate displacement equation (x) with respect to time once and to find acceleration of the plunger (a), differentiate displacement equation (x) twice, the procedure and final equations for velocity and acceleration of the plunger are shown in the below picture. 

Scotch Yoke mechanism - Displacement. velocity and acceleration analysis - Hand written notes

 Scotch Yoke mechanism - Displacement. velocity and acceleration analysis - Hand written notes

In this article Scotch Yoke Mechanism displacement, velocity and acceleration equations derived.

Watch it on YouTube: https://youtu.be/LHh7CEyqVKs

In the below picture shown is a typical Scotch yoke mechanism, Crank radius is R, angular velocity of omega is applied on the crank clock wise and angular acceleration of alpha is also applied on the crank, shown also counter clockwise. 

When crank rotates by an angle theta in the counter clockwise direction, plunger moves by a distance of x towards left. In the below pictures shown the procedure to find displacement of plunger x, velocity of plunger and acceleration of the plunger.

Four bar mechanism - Static force analysis - Problem 4

 Four bar mechanism - Static force analysis - Problem 4

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Q. The uniform bar of mass m is held in the inclined position theta by the horizontal force F applied to the links AB and BC whose masses are negligible, For the position shown where AB is perpendicular to AO and BC is perpendicular to the bar, determine F.

In the below picture shown is a mechanism and geometric parameters are shown. Mass of the bar OC is m and acts vertically downwards, A force of F is applied at point B. In this problem we need to derive an equation for the equilibrium of the mechanism's shown position.

Four bar mechanism - Static force analysis - Problem 3

 Four bar mechanism - Static force analysis - Problem 3

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Q. The couples C1 and C2 act on the linkage. Find the ratio C1/C2 for which the linkage will be in equilibrium in the position shown.

In the below picture shown is a four bar linkage and dimensions of different links are shown below. A couple C is applied at A and another couple C2 is applied at D. In this problem we need to find the ratio C1/C2 for the position shown.

Four bar mechanism - Static force analysis - Problem 2

 Four bar mechanism - Static force analysis - Problem 2

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Q. A horizontal force P is applied to the four bar mechanism shown. If the weight of the bars is negligible compared with the applied force P, determine the magnitude of the couple M needed to hold the mechanism in equilibrium at the orientation shown.

In the below picture shown is a four bar mechanism with link lengths, L1, L2, L3. Fixed link horizontal length is b and vertical height is h. A force of P is applied at B as shown in the below figure. In this problem we need to find the couple M at O to keep this mechanism in equilibrium.

In the below picture shown forces and reactions on the mechanism.

In the above picture show the procedure to derive equation containing M, P and geometric parameters of the mechanism. 

Four bar mechanism - Static force analysis - Problem 1

 Four bar mechanism - Static force analysis - Problem 1

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Q. Determine the force supported by the roller at D. Use the values a = 0.6 m, b = 1.2 m, c = 0.6 m, d = 0.3 m, h = 0.3 m and P = 200 N.

In the below picture shown is a four bar linkage with dimensions mentioned above. at D link BC is supported by a roller. on link OA a load P is applied as shown in below figure. In this problem we need to calculate reaction force at the roller.

In the below picture shown forces and reactions on the linkage.

Scotch Yoke mechanism - Displacement. velocity and acceleration analysis - Hand written notes

 Scotch Yoke mechanism - Displacement. velocity and acceleration analysis - Hand written notes

In this article for a variation of Scotch Yoke Mechanism displacement, velocity and acceleration equations derived.

Watch it on YouTube: https://youtu.be/BPfuK3Fw5ds

In the below picture shown is a variation of the scotch yoke mechanism, in which crank radius is r and radius of the sliding block is R. Omega is angular velocity of the crank and alpha is angular acceleration of the crank.

When crank rotates by an angle theta in counter clock wise direction, the plunger displaces by a distance S, in the below pictures described how to calculate plunger displacement, plunger velocity and plunger acceleration.

To find velocity of the plunger, differentiate displacement equation S with respect to time once and to find acceleration of the plunger differentiate displacement equation S twice with respect to time.

Scotch Yoke mechanism - Displacement. velocity and acceleration analysis - Hand written notes

 Scotch Yoke mechanism - Displacement. velocity and acceleration analysis - Hand written notes

In this article for a variation of  Scotch Yoke Mechanism displacement, velocity and acceleration equations derived.

Watch it on YouTube: https://youtu.be/jbpH45SriBs

In the below picture shown is a variation of Scotch Yoke Mechanism, where length of the crank is R, and angle between sliding block and plunger/horizontal axis is alpha. Omega is angular velocity and alpha is angular acceleration of the crank.

In the below picture, described how to derive equation to find displacement of the plunger (x) in terms of crank length R, crank angle theta and sliding block angle alpha.

To find the velocity of plunger (x dot), differentiate displacement equation (x) with respect to time once and to find acceleration of the plunger (x double dot), differentiate displacement equation (x) twice, the procedure and final equations for velocity and acceleration of the plunger are shown in the below picture. In the below equations omega is angular velocity of crank and "a" which is next to R is angular acceleration of the crank.

Scotch Yoke mechanism - Displacement. velocity and acceleration analysis - Hand written notes

 Scotch Yoke mechanism - Displacement. velocity and acceleration analysis - Hand written notes

In this article Scotch Yoke Mechanism displacement, velocity and acceleration equations derived.

Watch it on YouTube: https://youtu.be/W6KqZGLH3rQ

In the below picture shown is a typical Scotch yoke mechanism, Crank radius is R, angular velocity of omega is applied on the crank clock wise and angular deceleration of alpha is also applied on the crank, shown clockwise. 

When crank rotates by an angle theta in the counter clockwise direction, plunger moves by a distance of x towards left. In the below pictures shown the procedure to find displacement of plunger x, velocity of plunger and acceleration of the plunger.

Offset slider crank mechanism - Displacement, velocity and acceleration analysis - Hand written notes

Offset slider crank mechanism - Displacement, velocity and acceleration analysis - Hand written notes

Watch it on YouTube: https://youtu.be/dckGdtBxfCE

In the below picture shown is an Offset Slider crank mechanism, in which crank length is L2, coupler length is L3, crank angle is theta 2 and offset is "e" below the crank axis. Procedure to find coupler angle theta 3 and Slider displacement is described in the below pictures.

To find Velocity of the slider V, differentiate displacement equation x once with respect to time and to find acceleration of the slider A, differentiate displacement equation x with respect to time twice.

Procedure to find angular velocity omega 3 and angular acceleration alpha 3 of the coupler is described in the below picture.

Offset slider crank mechanism - Displacement, velocity and acceleration analysis - Hand written notes

 Offset slider crank mechanism - Displacement, velocity and acceleration analysis 

Watch it on YouTube: https://youtu.be/UpovHyIfygM

In the below picture shown is an Offset Slider crank mechanism, in which crank length is L2, coupler length is L3, crank angle is theta 2 and offset is "e" below the crank axis. Procedure to find coupler angle theta 3 and Slider displacement is described in the below pictures.

To find Velocity of the slider V, differentiate displacement equation x once with respect to time and to find acceleration of the slider A, differentiate displacement equation x with respect to time twice.

Procedure to find angular velocity omega 3 and angular acceleration alpha 3 of the coupler is described in the below picture.

Inline Slider Crank Mechanism - Position, Displacement, Velocity and Acceleration analysis

Inline Slider crank mechanism - Position, displacement, velocity and acceleration analysis

Watch it on YouTube: https://youtu.be/hS_VrVSpuZ4

In the below picture shown is an Inline Slider crank mechanism, in which crank length is L2, coupler length is L3, crank angle is theta 2. Procedure to find coupler angle theta 3 and Slider displacement is described in the below pictures.

To find Velocity of the slider V, differentiate displacement equation x once with respect to time and to find acceleration of the slider A, differentiate displacement equation x with respect to time twice.

Procedure to find angular velocity omega 3 and angular acceleration alpha 3 of the coupler is described in the below picture.