Swinging basket trebuchet
Here is a link to this design: Swinging Counterweight Trebuchet Some designs have proportionately long basket handles, and have a smoother post-launch.
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4 Feb The basket allows the weight to fall more vertically than if it were fixed since the basket is free to swing and will adjust its fall, to a degree.
How to Build a Trebuchet (with Pictures) - wikiHow
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The Hila Trebuchet
Description:To simplify the analysis here, the sling is replaced with a single cable in tension attached to the payload and the end of the beam. At a critical point one end of the sling slips off of a peg at the end of the throwing arm; if the sling length has been adjusted so that the missile is travelling at a 45 degree angle at that instant, the maximum distance can be achieved. This straight fall utilizes the gravitational energy of the falling mass more efficiently. Yep, you are not getting what you pay for. With the counterweight being able swing there will be more energy generated as the weight will fall with a more vertical motion than if it were fixed to the end of the arm and only moving in an arc.