how to extend solid features
How was the geometry created?
I would cut away some material from both sides, so that you have more area to work with. Then use a boundary feature to connect to two open faces. Within the boundary feature, choose curvature continuous as the end condition for both sides of the feature. This will only work if you create a sufficient gap between the bodies first. Curvature continuous for the end conditions will provide a smooth transition between the two bodies.
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I created something similar once and got the result like this. I was sweeping a circle on a spline that meets another sweep at the end.
Make sure the spline ends at the face of previous sweep, then use Minimum Twist and Align with end faces options in sweep command.
simple when you are creating a part which is to be continuous, first make a sketch of curves which may be combination of continuous lines, arcs etc as per the requirement and finish it. then again take another sketch in different plane normal to the first one and draw the required shape and finish it. then use sweep/swept feature select the required sketch and then select the guide/path which is your first sketch. you can have the design of which you desired