This paper deals with the synthesis of a second order parametrically c
ontinuous (C-2) motion that interpolates through a given set of config
urations of an object. It derives conditions for blending two motion s
egments with C-2 continuity and develops an algorithm for constructing
a C-2 composite Bezier type motion that has similarities to Beta-spli
nes in the field of Computer Aided Geometric Design. A criterion for e
valuating the smoothness of a motion is established and is used to syn
thesize a ''globally smooth'' motion. The results have applications in
trajectory generation in robotics, mechanical systems animation and C
AD/CAM.