Mechanism building CREATING OF KINEMATIC CHAINS Ing. Šimon Kovář, Ph.D. Planar Kinematic Chains Closed Composite Open Simple free free Combine Composite Open Simple free fixed Mechanism Building| 20.10.2015 Kinematics links Paternary link, Mechanism Building| 20.10.2015 Planar Kinematic Chain Grubler´s equation 푖 = 3 ∙ 푛 − 1 − 푗 ∙ 푑푗 i – DOF – Degrees of Freedom n – number of members of cinematic chain J – number of kinematic pairs dj – class of kinematic pairs Mechanism Building| 20.10.2015 Kinematic Chain with constrained motion A type of kinematic chain is one 푖 = 3 ∙ 푛 − 2 ∙ 푗 = 4 with constrained motion, which means that a definite motion of any link produces unique motion of all other links. Thus motion of any point on one link defines the relative position of any point on any other link. So it has one 3 ∙ 푛 − 4 degree of freedom. 푗 = 2 Mechanism Building| 20.10.2015 Kinematic Chain – Six members only rotation connection – kinematic pairs GRÜBLER'S EOUATION • The number of links in the mechanism must be even • The number of binary links in the mechanism must be greater or equal to four • The number of kinematic elements in one link cannot be greater than half of the number of links in the mechanism. 풏 m is the maximum number of kinematic elements on any 풎풎풂풙 = max ퟐ one link when the mechanism contains l links. 풏 = 풏ퟐ + 풏ퟑ ퟐ ∙ 풓 = ퟐ ∙ 풏ퟐ + ퟑ ∙ 풏ퟑ Ttwo kinematic elements are joined to form a kinematic pair. ퟑ ∙ 풏 − ퟒ 풊 = ퟑ ∙ 풏 − ퟏ − ퟐ ∙ 풓 풓 = ퟐ http://ocw.metu.edu.tr/pluginfile.php/3958/mod_resource/content/6/ch2/2-4.htm Mechanism Building| 20.10.2015 Kinematic Chain – Six members only rotation connection – kinematic pairs Mechanism Building| 20.10.2015 Kinematic Chain – Eight members GRÜBLER'S EOUATION Mechanism Building| 20.10.2015 Kinematic Chain – Eight members 1. skupina 9 variant Mechanism Building| 20.10.2015 Kinematic Chain – Eight members 2. skupina 5 variant Mechanism Building| 20.10.2015 Kinematic Chain – Eight members 3. skupina 2 varianty Mechanism Building| 20.10.2015 Kinematic Chain – Ten members Mechanism Building| 20.10.2015 Kinematic Chain – Ten members Mechanism Building| 20.10.2015 Kinematic Chain – Ten members Mechanism Building| 20.10.2015 Kinematic Chain – Ten members Mechanism Building| 20.10.2015 Kinematic Chain – Ten members Mechanism Building| 20.10.2015 Spatial mechanisms 3D kinematic chains 3D kinematic chains 푑 푖 = 6 ∙ 푛 − 푑 − 1 + 푖푗 1 n….. Number of members d….. Number of kinematic linkages ij ….. Degree of freedom of j- kinemativ pair 3D kinematic chains – example 1. 푑 푖 = 6 ∙ 푛 − 푑 − 1 + 푖푗 =? 1 3D kinematic chains – example 1. 푖 = 6 ∙ 4 − 4 − 1 + 1 + 3 + 1 + 2 = 1° 3D kinematic chains – example 2. 푑 푖 = 6 ∙ 푛 − 푑 − 1 + 푖푗 =? 1 3D kinematic chains – example 2. 푖 = 6 ∙ 4 − 4 − 1 + 1 + 2 + 1 + 3 = 1° 3D kinematic chains – example 3. 푑 푖 = 6 ∙ 푛 − 푑 − 1 + 푖푗 =? 1 3D kinematic chains – example 3. 푖 = 6 ∙ 4 − 4 − 1 + 1 + 3 + 3 + 1 = 2° 3D kinematic chains – example 4. 푑 푖 = 6 ∙ 푛 − 푑 − 1 + 푖푗 =? 1 3D kinematic chains – example 4. 푖 = 6 ∙ 4 − 4 − 1 + 1 + 2 + 3 + 1 = 1° 3D kinematic chains – example 5. Design kinematic links of the chain and check the number of degrees of freedom. Test equipment for testing heald shafts Shedding mechanism Shedding mechanism Shedding mechanism Shedding mechanism i= 6 ∙ 14 − 1 − 19 + 37 = 1° Steering Steering 푖 = 6 ∙ 14 − 18 − 1 + 38 = 8° Steering.