Introduction to Spatial Mechanism and applications of DH parameters in Spatial mechanism. Also introduction to Matrix Method.

1. Spatial mechanism
Name : Kaustubh S. Garud
Roll. No. 503006
Subject : ASOM
Guided by
Prof. S. T. Chavan

2. Introduction
• Mechanisms having three dimensional points
paths are called spatial mechanisms.
• If there is any relative motion that is not in the
same plane or in parallel planes, the
mechanism is called the spatial mechanism.
• Mobility of a kinematic chain can be obtained
from the Kutzbatch criterian which is
54321 2345)1(6 jjjjjnm 

9. • The coordinates of points G2 & G3 is written in
fixed coordinate system o1x1y1z1. The
coordinates of G2 are then

10. • The coordinates G3 will first be expressed with
respect to the system of axes , where
is parallel to x1 and axes is perpendicular to
both and z4 hence,
0
sin
cos
34
33
33



Gz
aG
aG


4R
4z
4R
44 zR 

12. • Using this now we can write coordinates of G3
with respect to o1x1y1z1 as
• The distance G2G3 which is equal to a2, so
writing in terms of the coordinates as

13. • By applications of trigonometric identities and
ordering terms this becomes

14. Symbolic Equations
• Symbolic notation allows the relative positions
of the axis of a mechanism to be completely
defined by specifying four parameters : a, α,θ
and s between each link and member

16. • Once the four parameters have been
established for each pair of linkage the
geometry of the linkage is completely
specified, and can be represented by a
symbolic equation of the form

21. Matrix method
• Once linkage has been described by means of
a symbolic equation, a rectangular coordinate
system is defined on each link.
• A change of coordinate or linear
transformation between adjacent system may
be represented by the 4 X 4 matrix ivolving
the parameters a, α,θ and s of the symbolic
equation.

28. References
• R. Hartenberg J. Denavit ‘Kinematic Synthesis
of mechanisms’
• Antonio Lopez-Gomez ‘Spatial Mechanisms:
Analysis and Systems’
• Shigley and Uicker ‘Theory of machines and
mechanism’

29. Thank you