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X-WR-CALNAME;VALUE=TEXT:EPS Seminar detail
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DTSTART:20161030T020000
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DTSTART:20170326T010000
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UID:calendar.1056.field_date_time.0@projects.eps.hw.ac.uk/seminars
DTSTAMP:20241007T231817Z
CREATED:20170320T152957Z
DESCRIPTION:Prof Andreas Müller\nLocation: SR 1.14\n\nSynopsis: \n\n\n\nThe
degree of freedom (DOF) and the mobility are essential kinematic features
of linkages. Although mobility analysis has been at the core of geometry
and theoretical kinematics since centuries\, it remains to develop general
ly applicable mobility criteria.\n\n\nThe finite (local) DOF of a linkage
is the (local) dimension of its configuration space (c-space) variety wher
eas the (instantaneous) differential DOF is the dimension of the kernel of
the constraint Jacobian. Despite being simple this definition is difficul
t to use. Recently the concept of tangent cone to the c-space modelled as
an analytic variety has been applied noting that its dimension equals the
local dimension of the c-space. It will be shown how the tangent cone (an
algebraic variety) can be computed from the joint screw coordinates of the
linkage. \n\n\nMost linkages exhibit kinematic singularities. A configura
tion is a kinematic singularity when the differential DOF changes\, otherw
ise it is a regular configuration. Singular configurations cannot be ident
ified by inspection of the rank of the constraint Jacobian. For instance\,
the c-space of so-called overconstrained linkages consists of manifolds w
ith rank deficient Jacobian. It is also not sufficient to compare the fini
te and differential DOF since this can be different in regular configurati
ons of underconstrained (shaky) mechanisms. It will be shown how kinematic
singularities can be established using the tangent cone to the varieties
of critical points of the constraint mapping. This provides a necessary an
d sufficient condition\, and eventually allows for a reconfiguration analy
sis of linkages.\nThe audience is expected to have a background in general
kinematics and preferably in screw and Lie group theory.
DTSTART;TZID=Europe/London:20170324T131500
DTEND;TZID=Europe/London:20170324T141500
LAST-MODIFIED:20170320T152957Z
SUMMARY:Mobility and Reconfiguration Analysis of Linkages
URL;TYPE=URI:https://projects.eps.hw.ac.uk/seminars/event/1056
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