A prismatic joint with twist ξ3 = (v3,0) is normal to a plane containing two parallel revolute axes ξi = (qi
×ωi,ωi), i = 1,2 if
• vT 3 ωi = 0
• vT 3 (q1 −q2) = 0
• ω1 = ±ω2
Show that when this occurs, any six degree of freedom manipulator is at a singular conﬁguration.
Give an example of a manipulator exhibiting such a singularity.
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