Rather than to find a "push to open slide" I prefer to install the "push to open catch" at the end of the frame.
The disadvantage of the slide is need the gap to install it, and each block will without joins, which is not strong enough to support people's weight.
(photo from Internet: For Handleless furniture )
Because there are limited product in Auckland land, I couldn't find the "catch " which can install to my 1:1 model. In order to show how the block will work with the "catch" at the end of the block, I took photos of each motion and combine them together to make an small animation.
I made each block has a join between each horizontal block. The joins can help the block slide well and with the joins the structure will be very strong.Blocks will be very stable, when people shake them.The force diagram is shown below. The joins is placed to horizontal line is because I want the top surface is flag without any gaps and each block just perfect fit to each other. Therefore, no joins between vertical blocks. All block are hollow, so when the block moves toward us, there will be a hole which people can put their finger in and help them to pull out the block. See the animation above.
The whole 1:1 model is about 500mm long, and each block is 150mm*1500mm large.The thickness of the frame is 50mm, joins are 30mm（height）*20mm(wideness)*500mm(long)
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