MEE 3025 MECHANISMS

WEEK 2

BASIC CONCEPTS

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.

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

b) Force Closed Kinematic Pairs: There is an external force keeping the two kinematic elements in contact (e.g. gravity, spring force).

A) Higher Kinematic Pairs: Contact at a point or on a line.

B) Lower Kinematic Pairs: Contact along a surface.

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

Planar Space:

Xa,Ya, or r,, Any three of X1, Y1, X2 or Y2

DOF=3, =3

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.

Link

• A rigid body that contains at least two kinematic elements.

Schematic representations for links.

Actual Shape of the Mechanism

Engineering Drawing for a Mechanism

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

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.

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.

Four bar mechanismDOF=1One Input:

Five bar mechanismDOF=2Two Inputs: ,

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.

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

Link 1 is fixed

General planar motion

(S,)

()

()

Degree of Freedom of a Mechanism, F

F = Degree of freedom without constraint – Number of constraints

General Degree-of-freedom Equation

=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