Chap.2 Kinematics fundamental
? 2.1 Basic Concept
? 2.2 Determining Degree of Freedom
? 2.3 How does a kinematic chains transform
into a mechanism?
? 2.4 Kinematic Diagram of Mechanism
? 2.5 Principle of Mechanism Constitution
2.1 Basic Concepts of Mechanisms
Degree of freedom (自由度 )
Link （ 构件）
Kinematic Pairs (Joints)（ 运动副）
Machine Element（ 机械零件）
Fixed link ( frame)（ 机架）
Crank,couple,rocker（ 曲柄、连杆、摇杆）
Kinematic Chain（ 运动链）
Mechanism（ 机构）
Machine（ 机器）
Degree of Freedom（ 自由度）
The system’s DOF is equal to the number of
independent parameters which are needed to
uniquely define its position in space at any
instant of time,
2.1Basic Concepts of Mechanisms(1)
Link（ 构件）,is a rigid body which possesses
at lease two nodes which are points for
attachment to other links,
nodes
Ternary link
Quaternary link Binary link
nodes
2.1Basic Concepts of Mechanisms(2)
Joint,is a connection between two or more links(at
their nodes),which allows some motion,or
potential motion,between the connected links,
Joints (also called kinematic pairs) can be classified in
several ways,
1,By the type of contact between the elements,line,
point,or surface,
2,By the number of degree of freedom allowed at
the joint,
3,Others
2.1Basic Concepts of Mechanisms(3)
Joint (铰链或运动副 )
Lower pairs（ 低副）,joints with surface contact
Prismatic joint Revolute joint Cylindric joint Spherical joint Helical joint Planar joint
Type P joint R joint C joint S joint H joint F joint
DOF 1 1 2 3 1 3
2.1Basic Concepts of Mechanisms(4)
Higher pairs（ 高副）,joints with point or line contact
2.1Basic Concepts of Mechanisms(5)
DOF 5 2
Examples of higher pairs
Force –closed
need external force
Form –closed
closed by its geometry
2.1Basic Concepts of Mechanisms(6)
Diagram of Kinematic pairs（ 运动副简图）
Prismatic joint Revolute joint Cylindric joint Spherical joint Helical joint
Type P joint R joint C joint S joint H joint
DOF 1 1 2 3 1
Diagram
2.1Basic Concepts of Mechanisms(7)
Machine Element（ 机械零件）, minimum
unit during manufacturing
2.1Basic Concepts of Mechanisms(8)
Binary link
This link has several
machine elements
*Kinematic Chain（ 运动链）, an assemblage of links
and joints,If these links are connected in such a way
that no motion is possible,a locked chain(structure)
result,
Mechanism（ 机构）, a kinematic chain in which at
lease one link has been,grounded”,or attached,to
the frame of reference(which itself may be in motion);
the links in the kinematic chain move upon each
other with definite relative motion,
Machine（ 机器）, a combination of resistant bodies
arranged to compel the mechanical forces of nature
to do work accompanied by determinate motion,
2.1Basic Concepts of Mechanisms(9)
Characteristics of a machine,
1,Composed of man-made elements
2,The elements are arranged to transmit motion
3,Can transmit energy,and fulfill certain work for
human being,
Constitution,
Parts of a machine,normally there are four parts,
namely,Motors and Drivers,Controller,Working part,
Transmission,
Crank(曲柄 ),a link which makes a complete revolution
and is pivoted to ground,
Rocker（ 摇杆）, a link which has oscillatory(back and
forth) rotation and is pivoted to ground,
Coupler(connecting rod,连杆 ),a link which has
complex motion and is not pivoted to ground,
Ground（ 机架）, any link or links that are fixed
(nonmoving) with respect to the reference frame,
( Note that reference frame may in fact itself be in
motion.)
2.1Basic Concepts of Mechanisms(10)
Crank
曲柄
Rocker
摇杆
Coupler
连杆
Frame or Ground
机架
2.1Basic Concepts of Mechanisms(11)
Fully rotating revolute;
Partially rotating revolute;
? Planar mechanism,all links of a mechanism
move in planes that remains parallel to each
other,Otherwise,it is a Spatial mechanism,
2.2 Determining Degree of Freedom
? 1,Degree of Freedom of a Mechanism
? 2,Kinematic Diagram of Mechanism
1,DOF of a Mechanism
1.1 Review the definition of DOF
1.2 Degree of freedom of a link
1.3 DOF formula of a planar mechanism
1.4 Points of Attention to Calculating DOF
1,DOF of a Mechanism
1.1 Definition
DOF, The number of independent coordinates
required to define its position,
1.2 Degree of freedom of a link
? Diagram of Links and Joints
? Diagram of Mechanisms
1,DOF of a Mechanism
1.3 DOF formula of a planar mechanism
M,degree of freedom or mobility
L,number of links
J1,number of 1 DOF joints
J2,number of 2 DOF joints
212)1(3 JJLM ????
1,DOF of a Mechanism
? Example,
1,DOF of a Mechanism
1.4 Points of Attention to Calculating DOF
A:Multiple joints(compound hinges)
B:Passive DOF
C:Redundant Constraints
Multiple joints(compound hinges)
A,Multiple joints(compound hinges)
B,Passive DOF
How many movable links,full joints and
half joints does it have?
DOF of cam mechanism=?
C,Redundant Constraints
2.3 How does a kinematic chains
transform into a mechanism?
?
Conclusion,
1) At least one link has been
grounded
2) DOF equals to the number
of the drivers
2.4 Kinematic Diagram of Mechanism
1,Definition and Purpose
The kinematic diagram serves a purpose similar to that of the
electrical schematic or circuit diagram in that it displays only the
essential skeleton of the mechanism,It embodies the key
dimensions that affect its motion and expresses their connection
between each others,
There are two forms,a sketch (proportional but not exactly to
scale),and the scaled kinematic diagram(usually used for further
analysis,position,displacement,velocity,acceleration,force and
torque transmission,etc)
2,How to draw?
2 Procedure for drawing the kinematic diagram of a
mechanism
? 1.Analyse the construction,motion of the mechanism;
Select a visual angle to observe the transmission route
from the driving links to output links,
? 2,Determine the type and number of kinematic pairs；
? 3,Choose a drawing plane to express themechanism；
? 4,Choose a proper scale (=actual length(m)/length in
diagram(mm)) to draw,Be careful about the relative
positions between the pairs,For convenient reference,
the links are numbered,while the joints are lettered,The
input and output are also labeled,
? 5,Calculate and check the degree of freedom of the
mechanism,
DOF,
3?7-2 ? 9-2=1
2.5 Composition Principle of Mechanism
? We know,
1,A mechanism can be divided into two parts,the
basic mechanism (one is the
frame+drivers+kinematic pairs(which connect the
frame and drivers)),the others are the left(driven
system),
2,DOF of a mechanism=number of the drivers
Then,DOF of the left= 0
Assur groups
Outer pairs
Inner pairs
Grade Ⅱ Assur groups
Assur groups
Grade Ⅲ Assur groups
? The DOF of the left group is zero,and no
group can be divided further into two or more
zero-DOF groups,then such groups are called
Assure groups,
? A mechanism can be assembled from a basic
mechanism by connecting Assur groups to
the determined links using outer pairs,group
by group,
Example
mechanism
Homework
1,Read book pp22-33,pp37 and pp55-59
2,Pp69 2-21(draw the kinematic diagram )
3,Calculate the DOF
? 2.1 Basic Concept
? 2.2 Determining Degree of Freedom
? 2.3 How does a kinematic chains transform
into a mechanism?
? 2.4 Kinematic Diagram of Mechanism
? 2.5 Principle of Mechanism Constitution
2.1 Basic Concepts of Mechanisms
Degree of freedom (自由度 )
Link （ 构件）
Kinematic Pairs (Joints)（ 运动副）
Machine Element（ 机械零件）
Fixed link ( frame)（ 机架）
Crank,couple,rocker（ 曲柄、连杆、摇杆）
Kinematic Chain（ 运动链）
Mechanism（ 机构）
Machine（ 机器）
Degree of Freedom（ 自由度）
The system’s DOF is equal to the number of
independent parameters which are needed to
uniquely define its position in space at any
instant of time,
2.1Basic Concepts of Mechanisms(1)
Link（ 构件）,is a rigid body which possesses
at lease two nodes which are points for
attachment to other links,
nodes
Ternary link
Quaternary link Binary link
nodes
2.1Basic Concepts of Mechanisms(2)
Joint,is a connection between two or more links(at
their nodes),which allows some motion,or
potential motion,between the connected links,
Joints (also called kinematic pairs) can be classified in
several ways,
1,By the type of contact between the elements,line,
point,or surface,
2,By the number of degree of freedom allowed at
the joint,
3,Others
2.1Basic Concepts of Mechanisms(3)
Joint (铰链或运动副 )
Lower pairs（ 低副）,joints with surface contact
Prismatic joint Revolute joint Cylindric joint Spherical joint Helical joint Planar joint
Type P joint R joint C joint S joint H joint F joint
DOF 1 1 2 3 1 3
2.1Basic Concepts of Mechanisms(4)
Higher pairs（ 高副）,joints with point or line contact
2.1Basic Concepts of Mechanisms(5)
DOF 5 2
Examples of higher pairs
Force –closed
need external force
Form –closed
closed by its geometry
2.1Basic Concepts of Mechanisms(6)
Diagram of Kinematic pairs（ 运动副简图）
Prismatic joint Revolute joint Cylindric joint Spherical joint Helical joint
Type P joint R joint C joint S joint H joint
DOF 1 1 2 3 1
Diagram
2.1Basic Concepts of Mechanisms(7)
Machine Element（ 机械零件）, minimum
unit during manufacturing
2.1Basic Concepts of Mechanisms(8)
Binary link
This link has several
machine elements
*Kinematic Chain（ 运动链）, an assemblage of links
and joints,If these links are connected in such a way
that no motion is possible,a locked chain(structure)
result,
Mechanism（ 机构）, a kinematic chain in which at
lease one link has been,grounded”,or attached,to
the frame of reference(which itself may be in motion);
the links in the kinematic chain move upon each
other with definite relative motion,
Machine（ 机器）, a combination of resistant bodies
arranged to compel the mechanical forces of nature
to do work accompanied by determinate motion,
2.1Basic Concepts of Mechanisms(9)
Characteristics of a machine,
1,Composed of man-made elements
2,The elements are arranged to transmit motion
3,Can transmit energy,and fulfill certain work for
human being,
Constitution,
Parts of a machine,normally there are four parts,
namely,Motors and Drivers,Controller,Working part,
Transmission,
Crank(曲柄 ),a link which makes a complete revolution
and is pivoted to ground,
Rocker（ 摇杆）, a link which has oscillatory(back and
forth) rotation and is pivoted to ground,
Coupler(connecting rod,连杆 ),a link which has
complex motion and is not pivoted to ground,
Ground（ 机架）, any link or links that are fixed
(nonmoving) with respect to the reference frame,
( Note that reference frame may in fact itself be in
motion.)
2.1Basic Concepts of Mechanisms(10)
Crank
曲柄
Rocker
摇杆
Coupler
连杆
Frame or Ground
机架
2.1Basic Concepts of Mechanisms(11)
Fully rotating revolute;
Partially rotating revolute;
? Planar mechanism,all links of a mechanism
move in planes that remains parallel to each
other,Otherwise,it is a Spatial mechanism,
2.2 Determining Degree of Freedom
? 1,Degree of Freedom of a Mechanism
? 2,Kinematic Diagram of Mechanism
1,DOF of a Mechanism
1.1 Review the definition of DOF
1.2 Degree of freedom of a link
1.3 DOF formula of a planar mechanism
1.4 Points of Attention to Calculating DOF
1,DOF of a Mechanism
1.1 Definition
DOF, The number of independent coordinates
required to define its position,
1.2 Degree of freedom of a link
? Diagram of Links and Joints
? Diagram of Mechanisms
1,DOF of a Mechanism
1.3 DOF formula of a planar mechanism
M,degree of freedom or mobility
L,number of links
J1,number of 1 DOF joints
J2,number of 2 DOF joints
212)1(3 JJLM ????
1,DOF of a Mechanism
? Example,
1,DOF of a Mechanism
1.4 Points of Attention to Calculating DOF
A:Multiple joints(compound hinges)
B:Passive DOF
C:Redundant Constraints
Multiple joints(compound hinges)
A,Multiple joints(compound hinges)
B,Passive DOF
How many movable links,full joints and
half joints does it have?
DOF of cam mechanism=?
C,Redundant Constraints
2.3 How does a kinematic chains
transform into a mechanism?
?
Conclusion,
1) At least one link has been
grounded
2) DOF equals to the number
of the drivers
2.4 Kinematic Diagram of Mechanism
1,Definition and Purpose
The kinematic diagram serves a purpose similar to that of the
electrical schematic or circuit diagram in that it displays only the
essential skeleton of the mechanism,It embodies the key
dimensions that affect its motion and expresses their connection
between each others,
There are two forms,a sketch (proportional but not exactly to
scale),and the scaled kinematic diagram(usually used for further
analysis,position,displacement,velocity,acceleration,force and
torque transmission,etc)
2,How to draw?
2 Procedure for drawing the kinematic diagram of a
mechanism
? 1.Analyse the construction,motion of the mechanism;
Select a visual angle to observe the transmission route
from the driving links to output links,
? 2,Determine the type and number of kinematic pairs；
? 3,Choose a drawing plane to express themechanism；
? 4,Choose a proper scale (=actual length(m)/length in
diagram(mm)) to draw,Be careful about the relative
positions between the pairs,For convenient reference,
the links are numbered,while the joints are lettered,The
input and output are also labeled,
? 5,Calculate and check the degree of freedom of the
mechanism,
DOF,
3?7-2 ? 9-2=1
2.5 Composition Principle of Mechanism
? We know,
1,A mechanism can be divided into two parts,the
basic mechanism (one is the
frame+drivers+kinematic pairs(which connect the
frame and drivers)),the others are the left(driven
system),
2,DOF of a mechanism=number of the drivers
Then,DOF of the left= 0
Assur groups
Outer pairs
Inner pairs
Grade Ⅱ Assur groups
Assur groups
Grade Ⅲ Assur groups
? The DOF of the left group is zero,and no
group can be divided further into two or more
zero-DOF groups,then such groups are called
Assure groups,
? A mechanism can be assembled from a basic
mechanism by connecting Assur groups to
the determined links using outer pairs,group
by group,
Example
mechanism
Homework
1,Read book pp22-33,pp37 and pp55-59
2,Pp69 2-21(draw the kinematic diagram )
3,Calculate the DOF
