Partitioning sublists based on positions, with new partitions immediately following original sublist

Question

I need to restructure this list nums:

nums = {{0.0140242, 0.138626, 0.0585034, 0.0509646, 0.0629815, 0.0750587, 
  0.00588226, 0.272169, 1.},
 {0.153123, 0.212751, 0.217497, 0.12154, 0.210508, 0.189625, 0.0680384, 
  0.0768402, 0.172107},
 {0.20766, 0.246923, 0.0924592, 0.142682, 0.110408, 0.20464, 0.246233, 
  0.251928, 0.07382}};

based on the following rules:

• Every 2nd element in each sublist should be moved/appended to a new vector immediately following its original vector
• Every 3rd element in each sublist should be moved/appended to a new vector immediately following its original vector and the 2nd elements vector

The resulting list should look like:

{{0.0140242, 0.0509646, 0.00588226},
 {0.138626, 0.0629815, 0.272169},         // new 2nd elements vector
 {0.0585034, 0.0750587, 1.},              // new 3rd elements vector
 {0.153123, 0.12154, 0.0680384},
 {0.212751, 0.210508, 0.0768402},         // new 2nd elements vector
 {0.217497, 0.189625, 0.172107},          // new 3rd elements vector
 {0.20766, 0.142682, 0.246233},
 {0.246923, 0.110408, 0.251928},          // new 2nd elements vector
 {0.0924592, 0.20464, 0.07382}}           // new 3rd elements vector

Answer 1

Join @@ Transpose[nums[[All, # ;; ;; 3]] & /@ {1, 2, 3}]

{{0.0140242, 0.0509646, 0.00588226},
{0.138626, 0.0629815, 0.272169},
{0.0585034, 0.0750587, 1.},
{0.153123, 0.12154, 0.0680384},
{0.212751, 0.210508, 0.0768402},
{0.217497, 0.189625, 0.172107},
{0.20766, 0.142682, 0.246233},
{0.246923, 0.110408, 0.251928},
{0.0924592, 0.20464, 0.07382}}

Also

Flatten[Partition[nums, {3, 3}], {3, 4, 1}]

same result

Answer 2

Flatten[Transpose@Partition[#,3]&/@nums,1]     

{{0.0140242,0.0509646,0.00588226},
{0.138626,0.0629815,0.272169},
{0.0585034,0.0750587,1.},
{0.153123,0.12154,0.0680384},
{0.212751,0.210508,0.0768402},
{0.217497,0.189625,0.172107},
{0.20766,0.142682,0.246233},
{0.246923,0.110408,0.251928},
{0.0924592,0.20464,0.07382}}