mee 3025 mechanisms week 2 basic concepts. mechanisms a group of rigid bodies connected to each...
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MEE 3025 MECHANISMS
WEEK 2
BASIC CONCEPTS
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Mechanisms
• A group of rigid bodies connected to each other by rigid kinematic pairs (joints) to transmit force and motion.
• Kinematic Element: Part of a rigid body used to connect it to another rigid body.
• Kinematic Pair (Joint): Pair of kinematic elements kept in a contact, so that there exists a relative motion between them.
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Classification of Kinematic Pairs
2) Closed kinematic pairs a) Form Closed kinematic pairs: One of the kinematic elements envelopes the other.
1) Open kinematic pairs
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b) Force Closed Kinematic Pairs: There is an external force keeping the two kinematic elements in contact (e.g. gravity, spring force).
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A) Higher Kinematic Pairs: Contact at a point or on a line.
B) Lower Kinematic Pairs: Contact along a surface.
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Degree of Freedom
Degree of Freedom of Space: The number of independent parameters required to defineposition of a rigid body in that space
Spatial Space:
Any six of, Xi, Yi, Zi, i=1,2,3 Xa,Ya,Za, and any two of 1, 2, 3
DOF=6, =6
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Planar Space:
Xa,Ya, or r,, Any three of X1, Y1, X2 or Y2
DOF=3, =3
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Degree-of-Freedom of a Kinematic Pair
• The number of independent parameters that is required to determine the relative position of one rigid body with respect to the other body connected by the kinematic pair.
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Link
• A rigid body that contains at least two kinematic elements.
Schematic representations for links.
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Actual Shape of the Mechanism
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Engineering Drawing for a Mechanism
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Kinematic Chain
• Links connected to each other by kinematic pairs.
• A mechanism is a kinematic chain with one of the links as fixed.
• a) Open kinematik chains• b) Closed kinematic chains
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Degree of a Joint
• Number of links connected at the joint minus one.
Degree of a joint is equal to the number of joints at that connection.Degree of freedom of a joint is the number of independent parameters required to define the position of one link relative to the other connected by that joint.
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Link Dimensions
• All dimensions are necessary for production, but not for the kinematic analysis. For a simple binary link for example, only length of the link is necessary kinematically. The length is the "kinematic dimension" of the link.
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Four bar mechanismDOF=1One Input:
Five bar mechanismDOF=2Two Inputs: ,
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Degree of Freedom of a Mechanism
Number of independent parameters required todefine the position of every link in thatmechanism.Degree of freedom of a mechanism depends on:• The degree of freedom of space• The degree of freedom of the joints• The number of links and joints • The distribution of links and joints • Does not depend on the shape of the links.
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Determination of the Degree-of- Freedom of a Mechanism
Let• =Degree of freedom of the mechanism’s space• (=6 for spatial space)• (=3 for planar and spherical space)• = Number of links in the mechanism • J = Number of joints in the mechanism• fi = Degree-of-freedom of the i th joint• F = Degree-of-freedom of the mechanism
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Link 1 is fixed
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General planar motion
(S,)
()
()
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Degree of Freedom of a Mechanism, F
F = Degree of freedom without constraint – Number of constraints
General Degree-of-freedom Equation
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=3
F=3(6-7-1)+7=1
• =Degree of freedom of the mechanism’s space
• (=6 for spatial space)• (=3 for planar and spherical space)• l= Number of links in the mechanism • J = Number of joints in the
mechanism• fi = Degree-of-freedom of the i th
joint• F = Degree-of-freedom of the
mechanism