SEMINAR PRESENTATION

PRESENTED BY:(GROUP 1)

ASHISH KUMAR KHETAN 05010305KALLA SIDDHARTH 05010318

RISHUB DEV 05010354

TITLE: A novel geometric and analytic technique for thesingularity analysis of one-dof planar mechanisms

AUTHOR: Raffaele Di Gregorio

INTRODUCTION TO SINGULARITY

• What is a singularity• When does a singularity occur• Why is singularity analysis important

TYPES OF SINGULARITIES

• Type I singularityInverse instantaneous

kinematic problemOutput variable reaches the

border of its range (dead centre)

Gives infinite mechanical advantage

At least one component of output torque equilibrated by the mechanism structure

Type I singularityType II singularityType III singularity

Fig 1: Type I singularity in a 4-bar mechanism

TYPES OF SINGULARITIES

• Type II singularityDirect instantaneous

kinematic problem Input variable reaches the

border of its range (dead centre)

Gives null mechanical advantage

Possibility of breakdown of the mechanism

Type I singularityType II singularityType III singularity

Fig 2: Type II singularity in a 4-bar mechanism

Fig 3: Type II singularity in a slider crank mechanism

TYPES OF SINGULARITIES

• Type III singularityThe input-output

instantaneous relationship does not hold

Instantaneous mobility is greater than the full cycle mobility

Occur for particular sizes of the links

Type I singularityType II singularityType III singularity

INPUT-OUTPUT RELATIONSHIPS

• Instantaneous input-output relationship of one dof mechanisms is linear

• Two types of motion are possible – translatory and rotatory

• Rotation – revolute pair• Translation – prismatic pair

INPUT-OUTPUT RELATIONSHIPS

• The following 4 cases need to be considered1. Input rotation, output rotation2. Input rotation, output translation3. Input translation, output rotation4. Input translation, output translation

INSTANTANEOUS CENTRE METHOD

• Instantaneous centre method is used for analysis.

• For n links, there are n(n-1)/2 instantaneous centres of rotation

• For a general four bar mechanism, the instantaneous centres are found as shown-

NOTATIONS USED

• i : for the input link• o : for the output link• f : for the reference link used to evaluate the

rate of input variable• k : for the reference link used to evaluate the

rate of output variable• Cio : instantaneous centre of link i and o

Fig 4: Positions of instantaneous centres for 4-bar mechanism

ANALYSIS USING INSTANTANEOUS CENTRE OF ROTATION

• Using the basic property of the instantaneous centre, we get

fVoi,o = fVoi,i

kVoi,o = kVoi,i

• ωif + ωok = ωof + ωik

ANALYSIS USING INSTANTANEOUS CENTRE OF ROTATION

• Using these relationships, we get

ANALYSIS USING INSTANTANEOUS CENTRE OF ROTATION

• Comparing the last equation with

a = (Cof – Cif)(Coi – Cik)

b = (Cok – Cik)(Coi – Cof)

ANALYSIS USING INSTANTANEOUS CENTRE OF ROTATION

• For Type I singularity, a = 0. This implies that at least one of the two geometric conditions should be satisfied –

Cof = Cif

Coi = Cik

ANALYSIS USING INSTANTANEOUS CENTRE OF ROTATION

• For Type II singularity, b = 0. This implies that at least one of the two geometric conditions should be satisfied –

Cok = Cik

Coi = Cof

ANALYSIS USING INSTANTANEOUS CENTRE OF ROTATION

• For Type III singularity, a and b simultaneously become zero.

ANALYSIS OF 4-BAR MECHANISM

ANALYSIS OF 4-BAR MECHANISM

• Type I singularity occurs when C42 coincides with C21 and thus input and coupler links become parallel

• Type II singularity occurs when C42 coincides with C41 and thus output and coupler links become parallel

• Type III singularity occurs when both the above conditions are satisfied and the mechanism becomes flattened

CONCLUSION

• Analysis of the singularities is essential for the design of a mechanism in order to get the desired output