Analysis of Non-Grashof Linkages:
In the figure, posted below, a four-bar Non-Grashof Linkage is shown. The same will be analysed and we will see what are it's limitations. There will be four Limiting phases in this type of Linkages, all the four, for this specific figure have been drawn on a Solid Edge Cad-software and are to the scale. The dark lines are that of the Linkage at rest and the dotted lines show the four positions of the linkage as it moves.
From the figure it can be seen when point A moves through the Arc A1A2A3A4 and comes back at A1, point B moves through Arc B1B2B3B4 and comes back to B1. It can also be seen that when A is at point A1 or A4 the links 3 and 4 become collinear there is a phase of non-rotation i.e. the link 2 comes to a standstill position, unable to move the combination of Link3 and Link4 (since they are lying in a straight line). Under the circumstances, when link-2 is in a position where it can neither rotate clockwise nor anti-clockwise the position is known as a Dead Centre Phase. Similarly point B also has two Dead-Centre-Phases
In order to understand the meaning of the Dead-Centre-Phase, let's try to bring in the issue of transmission of load, which is what all linkages are required to do in practical applications.
Assuming that there is no frictional loss, the effect of inertia and acceleration are also being omitted to simplify the matter. It is noteworthy that link-3 is a two-force member and transmits force between A and B only in tension or compression. Considering Link-2 to be the driver and link-4 to be the follower, if the Link-4 is to be driven clockwise against torque T4 then for equilibrium of link-4, the sum of torque about point C should be = 0. The equation of force F34 (force acting on point B in anticlockwise direction)
F34 = T4/ h = T4/CB x Sinδ
Where F34 = magnitude of force exerted by Link-3 on link-4
From the equation, above, it can be seen, for a given magnitude of force T4, the force acting at A, at B and along the link-3 will be minimum when δ = 90°and will increase as δ decreases, thus becoming infinite when δ = 0°.
The angle δ (when acute) the angle between the line of the action of force on the driven link (F34) and the line of hinges (CB) is known as the angle of transmission.
It can be seen, the angle of transmission become = 0 when the links are at dead-centre-phases. As such it is not a desirable phase in most of the mechanisms.
In the next section the Grashof Linkage will be analysed and you will be able to make a distinction between the two vis-a-vis their usages.
In the figure, posted below, a four-bar Non-Grashof Linkage is shown. The same will be analysed and we will see what are it's limitations. There will be four Limiting phases in this type of Linkages, all the four, for this specific figure have been drawn on a Solid Edge Cad-software and are to the scale. The dark lines are that of the Linkage at rest and the dotted lines show the four positions of the linkage as it moves.
From the figure it can be seen when point A moves through the Arc A1A2A3A4 and comes back at A1, point B moves through Arc B1B2B3B4 and comes back to B1. It can also be seen that when A is at point A1 or A4 the links 3 and 4 become collinear there is a phase of non-rotation i.e. the link 2 comes to a standstill position, unable to move the combination of Link3 and Link4 (since they are lying in a straight line). Under the circumstances, when link-2 is in a position where it can neither rotate clockwise nor anti-clockwise the position is known as a Dead Centre Phase. Similarly point B also has two Dead-Centre-Phases
In order to understand the meaning of the Dead-Centre-Phase, let's try to bring in the issue of transmission of load, which is what all linkages are required to do in practical applications.
Assuming that there is no frictional loss, the effect of inertia and acceleration are also being omitted to simplify the matter. It is noteworthy that link-3 is a two-force member and transmits force between A and B only in tension or compression. Considering Link-2 to be the driver and link-4 to be the follower, if the Link-4 is to be driven clockwise against torque T4 then for equilibrium of link-4, the sum of torque about point C should be = 0. The equation of force F34 (force acting on point B in anticlockwise direction)
F34 = T4/ h = T4/CB x Sinδ
Where F34 = magnitude of force exerted by Link-3 on link-4
From the equation, above, it can be seen, for a given magnitude of force T4, the force acting at A, at B and along the link-3 will be minimum when δ = 90°and will increase as δ decreases, thus becoming infinite when δ = 0°.
The angle δ (when acute) the angle between the line of the action of force on the driven link (F34) and the line of hinges (CB) is known as the angle of transmission.
It can be seen, the angle of transmission become = 0 when the links are at dead-centre-phases. As such it is not a desirable phase in most of the mechanisms.
In the next section the Grashof Linkage will be analysed and you will be able to make a distinction between the two vis-a-vis their usages.
No comments:
Post a Comment