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