Offset circular cam | Eccentric circular cam | Circular cam with Knife edge follower

 Offset circular cam | Eccentric circular cam | Circular cam with Knife edge follower

In this blog offset circular / eccentric circular / circular cam with knife edge follower position, velocity and acceleration equations derived using analytical method.

In the below picture shown is an eccentric circular disc cam with knife edge follower. Radius of the circular disc is R, eccentricity is r. Cam at its lowest position is shown in below picture. So the distance between follower knife edge to cam center is R-r.

When cam rotates by angle theta clockwise direction, the follower will be lifted up. In the below pictures described the procedure to calculate this cam lift for any given angle theta. To find velocity of the follower V, differentiate cam position equation x with respect to time once and to find acceleration of the follower A, differentiate x with respect to time twice. In the below equations omega is angular velocity of the cam and alpha is angular acceleration of the cam.

Offset circular cam | Eccentric circular cam | Circular cam with Flat faced follower

 Offset circular cam | Eccentric circular cam | Circular cam with Flat faced follower

In this blog offset circular / eccentric circular / circular cam with flat faced follower position, velocity and acceleration equations derived using analytical method.

In the below picture shown is an eccentric circular disc cam with flat faced follower. Radius of the circular disc is R, eccentricity is r. Cam at its lowest position is shown in below picture. So the distance between follower flat face to cam center is R-r.

When cam rotates by angle theta clockwise direction, the follower will be lifted up.in the below pictures described the procedure to calculate this cam lift for any given angle theta. To find velocity of the follower V, differentiate cam position equation x with respect to time once and to find acceleration of the follower A, differentiate x with respect to time twice. In the below equations omega is angular velocity of the cam and alpha is angular acceleration of the cam.

Four bar linkage | Four bar mechanism | Acceleration equations | Analytical method

 Four bar linkage / mechanism Acceleration equations

In this blog hand written notes of four bar mechanism acceleration equations derived using analytical method are attached 

To find angular acceleration of coupler link and angular acceleration of follower link, differentiate position equations twice with respect to time and follow the procedure described below.

The above equations are same for a four bar mechanism of any orientation.

Four bar Linkage | Four bar mechanism | Velocity equations | Analytical method

 Four bar linkage / Mechanism velocity equations

In this blog hand written notes of four bar mechanism velocity equations derived using analytical method are attached 

In the below picture shown a typical four bar mechanism (Crank rocker), L2 is crank length, L3 coupler length, L4 follower length and L1 is fixed link (frame) length. Angle between crank and horizontal axis is theta 2, angle between coupler and horizontal axis is theta 3, angle between follower link and horizontal axis is theta 4.

In the below picture described graphical method to find velocity of coupler and velocity of follower links. To find angular velocities of the links use the equations shown below.

To find angular velocity of the coupler and follower links, differentiate position equations with respect to time once and follow the procedure described below.

The above equations are same for a four bar mechanism of any orientation.

Inclined Four bar linkage | Four bar mechanism | Position and displacement analysis

  Four bar linkage / mechanism position and displacement analysis - Analytical method

Watch it on YouTube: https://youtu.be/oKspnxARe1s

In the below picture shown a typical four bar mechanism (Crank rocker), L2 is crank length, L3 coupler length, L4 follower length and L1 is fixed link (frame) length. Angle between crank and horizontal axis is theta 2, angle between coupler and horizontal axis is theta 3, angle between follower link and horizontal axis is theta 4 angle between fixed link (frame) and horizontal axis is theta (Counter Clockwise).

In the below pictures described the procedure to calculate coupler angle theta 3, follower link angle theta 3. 

In the below picture described the procedure to find position of the follower link i.e. position of the point C for any given crank angle theta 2. Position of point be can be calculated as Bx = L2 x Cos (theta2), By = L2 x Sin (theta2)

Inclined Four bar linkage | Four bar mechanism | Position and displacement analysis

 Four bar linkage / mechanism position and displacement analysis - Analytical method

Watch it on YouTube: https://youtu.be/vCN45AFRRYY

In the below picture shown a typical four bar mechanism (Crank rocker), L2 is crank length, L3 coupler length, L4 follower length and L1 is fixed link (frame) length. Angle between crank and horizontal axis is theta 2, angle between coupler and horizontal axis is theta 3, angle between follower link and horizontal axis is theta 4 angle between fixed link (frame) and horizontal axis is theta (Clockwise).

In the below pictures described the procedure to calculate coupler angle theta 3, follower link angle theta 3. 

In the below picture described the procedure to find position of the follower link i.e. position of the point C for any given crank angle theta 2. Also given equations to find position of the point B on the crank.

Four bar linkage | Four bar mechanism | Position and displacement analysis

 Four bar linkage / mechanism position and displacement analysis - Analytical method

In the below picture shown a typical four bar mechanism (Crank rocker), L2 is crank length, L3 coupler length, L4 follower length and L1 is fixed link (frame) length. Angle between crank and horizontal axis is theta 2, angle between coupler and horizontal axis is theta 3, angle between follower link and horizontal axis is theta 4.

In the below pictures described the procedure to calculate coupler angle theta 3, follower link angle theta 3 and transmission angle gamma using analytical method.

In the below picture described the procedure to find position of the follower link i.e. position of the point C for any given crank angle theta 2. Also given equations to find position of the point B on the crank.

Inclined - Offset Slider Crank Mechanism - Position, Displacement, Velocity and Acceleration analysis

 Inclined - Offset Slider Crank Mechanism - Position, Displacement, Velocity and Acceleration analysis

In this blog Inclined offset slider crank mechanism displacement, velocity and acceleration equations derived using analytical method.

In the below picture shown is a slider crank mechanism, crank length is L2, coupler length is L3 and slider is inclined by an angle theta 1 from the horizontal. Slider displacement axis is offset by a distance e below the crank axis. So, it is an inclined offset slider crank mechanism. 

In the below pictures described the procedure to calculate coupler angle, coupler angular velocity and coupler angular acceleration. In the below equations omega 3 is angular velocity of the coupler link and alpha 3 is angular acceleration of the coupler link.

When crank rotates by an angle theta 2 from horizontal, slider moves by a distance S from its extreme position. In the below picture described procedure to calculate this displacement of the slider S. To find slider velocity, differentiate displacement equation with respect to time once and to calculate slider acceleration, differentiate slider displacement equation with respect to time twice. In the below equations omega 2 is angular velocity of crank and alpha 2 angular acceleration of the crank.

Inclined - Offset Slider Crank Mechanism - Position, Displacement, Velocity and Acceleration analysis

  Inclined - Offset Slider Crank Mechanism - Position, Displacement, Velocity and Acceleration analysis

In this blog Inclined offset slider crank mechanism displacement, velocity and acceleration equations derived using analytical method.

In the below picture shown is a slider crank mechanism, crank length is L2, coupler length is L3 and slider is inclined by an angle theta 1 from the horizontal. Slider displacement axis is offset by a distance e above the crank axis. So, it is an inclined offset slider crank mechanism. 

In the below pictures described the procedure to calculate coupler angle, coupler angular velocity and coupler angular acceleration. In the below equations omega 3 is angular velocity of the coupler link and alpha 3 is angular acceleration of the coupler link.

When crank rotates by an angle theta 2 from horizontal, slider moves by a distance S from its extreme position. In the below picture described procedure to calculate this displacement of the slider S. To find slider velocity, differentiate displacement equation with respect to time once and to calculate slider acceleration, differentiate slider displacement equation with respect to time twice. In the below equations omega 2 is angular velocity of crank and alpha 2 angular acceleration of the crank.

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

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

In this blog Inclined inline slider crank mechanism displacement, velocity and acceleration equations derived using analytical method.

Watch it on YouTube: https://youtu.be/gexzl8bIsxk

In the below picture shown is a slider crank mechanism, crank length is L2, coupler length is L3 and slider is inclined by an angle theta 1 from the horizontal. Slider displacement axis coincides with the crank axis. so, it is an inclined inline slider crank mechanism. 

When crank rotates by an angle theta 2 from horizontal, slider moves by a distance S from its extreme position. In the below picture described procedure to calculate this displacement of the slider S.

In the below pictures described the procedure to calculate slider velocity and slider acceleration. To find slider velocity, differentiate displacement equation with respect to time once and to calculate slider acceleration, differentiate slider displacement equation with respect to time twice. In the below equations omega 2 is angular velocity of crank and alpha 2 angular acceleration of the crank.

In the below pictures described the procedure to calculate coupler angle, coupler angular velocity and coupler angular acceleration. In the below equations omega 3 is angular velocity of the coupler link and alpha 3 is angular acceleration of the coupler link.