(SEM VIII) THEORY EXAMINATION 2016-17 ADVANCE SYNTHESIS OF MECHANISMS

SECTION A (Brief Answers)

Degree of Freedom
Degree of freedom (DOF) is the number of independent motions required to define the position of a mechanism. For planar mechanisms, it is calculated using Gruebler’s equation.

Transmission Angle
Transmission angle is the angle between the coupler and follower link in a four-bar mechanism. It affects force transmission efficiency and should ideally be close to 90°.

Dimensional Synthesis
Dimensional synthesis involves determining the dimensions of mechanism links to achieve a desired motion or function.

Equation for Coupler Curve
The coupler curve equation describes the path traced by a point on the coupler link. It is derived using loop closure equations of the four-bar linkage.

Chebyshev Spacing
Chebyshev spacing is a method used to select accuracy points in function generation to minimize structural error over a range of motion.

Coupler Curve
A coupler curve is the trajectory traced by any point on the coupler link of a four-bar mechanism during motion.

Mechanical Error
Mechanical error is the deviation between desired output and actual output in a synthesized mechanism.

Approximate Mechanism
An approximate mechanism achieves desired motion at selected accuracy points but may have errors between those points.

Freudenstein’s Equation for Velocity Analysis
Freudenstein’s equation relates input and output link angles in a four-bar mechanism and can be differentiated to obtain velocity relationships.

Exact Straight Line Mechanism
Exact straight-line mechanisms generate perfect straight-line motion without approximation, such as Peaucellier mechanism.

SECTION B (Medium Length Answers)

Five Accuracy Points Synthesis of Crank and Follower
In five-point synthesis, five desired positions of follower are selected. Using Freudenstein’s equation and Chebyshev spacing, link lengths are calculated so that mechanism passes through all specified accuracy points.

Four Bar Function Generator with Three Accuracy Points
In three-point synthesis, three pairs of input-output angles are selected. Using Freudenstein’s equation, constants are determined and link dimensions are calculated to satisfy these conditions.

Slider Crank Design
The design ensures that given crank displacements produce required slider displacements. Using displacement equations and geometry of slider crank, link dimensions are obtained.

Planar and Spatial Mechanism
A planar mechanism moves in a single plane, like four-bar linkage. A spatial mechanism moves in three dimensions, like universal joint. Each has specific industrial applications.

Cognate Linkages
Cognate linkages are three different linkages that generate the same coupler curve. They are useful in design flexibility.

Four Bar Linkage for Three Positions
To design linkage for three positions, graphical or analytical methods are used. Fixed pivots are located using perpendicular bisector method.

Instantaneous Centres
Instantaneous centres are points where relative velocity between two links is zero. They are located using Kennedy’s theorem.

Angular Displacement Design
Using Freudenstein’s equation, link dimensions are determined such that specified crank rotations produce desired follower rotations.

SECTION C (15-Mark Style Answers)

Slider Crank with Chebyshev Spacing
For proportional relationship between slider displacement and square of crank rotation, three Chebyshev accuracy points are selected within given range. Using displacement equation and loop closure relation, link lengths are calculated to minimize error.

Four Bar Synthesis for Function Generation
Given function Y = X¹·⁵, three accuracy points are selected. Using Freudenstein’s equation and initial angular conditions, constants are solved to determine link lengths satisfying function generation.

Approximate and Exact Straight Line Mechanisms
Approximate straight-line mechanisms like Watt’s mechanism generate near straight-line motion. Exact mechanisms like Peaucellier generate perfect straight-line motion using special linkage geometry.