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 define position 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 mechanism DOF=1 One Input:  Five bar mechanism DOF=2 Two Inputs: , 

Degree of Freedom of a Mechanism Number of independent parameters required to define the position of every link in that mechanism. 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