Mechanisms and Multibody Systems MECH3422

Lecture 2

Mobility

Definitions Mobility: the number of input parameters which

must be controlled independently in order to bring the device into a particular position (from Theory of Machines and Mechanisms 1995 by J.E. Shigley and J.J.Uicker)

Mobility (of a mechanism): the minimum number of

coordinates needed to specify the positions of all members of the mechanism relative to a particular member chosen as the base or frame (from Kinematics, Dynamics and Design of Machinery 2004 by K.J. Waldron and G.L. Kinzel)

JOINTS (KINEMATIC PAIRS): Lower

Copied from Kinematics, Dynamics and Design of Machinery 2004 by K.J. Waldron and G.L. Kinzel)

JOINTS (KINEMATIC PAIRS): Higher (some)

Copied from Kinematics, Dynamics and Design of Machinery 2004 by K.J. Waldron and G.L. Kinzel)

SOME COMPOUND JOINTS (typically considered as lower pairs)

Copied from Kinematics, Dynamics and Design of Machinery 2004 by K.J. Waldron and G.L. Kinzel)

2-D

MOBILITY CALCULATION

m 3(n1) 2 f1 1f2

m 6(n1) 5 f1 4 f2 3 f3 2 f4 1 f5

3-D

Kutzbach criterion

Spatial Mechanism: DELTA robot

(Tohoku University, Sendai, Japan) UWAs NUWAR robot has similar general structure

What are the number of members, the number of joints (kinematic pairs) and mobility (3-D) of the Delta robot shown below

No. of members:

Number of joints:

Mobility:

m 6(n1) 5 f1 4 f2 3 f3 2 f4 1 f5

Stewart Platform

Downloaded (GNU license)

from http://en.wikipedia.org/wiki/File:Hexapod_general_Anim.gif.

Artist: UtzOnBike.

Stewart Platform: driving simulator

Traffic Safety and Nuisance Research Institute, Tokyo, Japan

Stewart Platform: driving simulator

Traffic Safety and Nuisance Research Institute, Tokyo, Japan

Stewart Platform: driving simulator

Traffic Safety and Nuisance Research Institute, Tokyo, Japan

What are the number of members, the number of joints (kinematic pairs) and mobility (3-D) of the robot (Stewart platform) shown

below

No. of members:

Number of joints:

Mobility:

m 6(n1) 5 f1 4 f2 3 f3 2 f4 1 f5

Another Example of Linkage With Idle DOF: Cam with roller follower

Idle DOF

Kutzbach Criterion (mobility equation)

m=0 -> statically determinate structure

m statically indeterminate structure

m1 -> mechanism

Mechanisms the satisfy the mobility equation are referred to as properly constrained

But sometimes the results are incorrect

Overconstrained mechanisms: mobility equation

underestimates the true mobility; usually giving

negative values (as in case of 4-bar linkage in 3-D)

Mechanisms with idle degrees of freedom: mobility equation overestimates the true mobility

(as in case of Stewart platform)