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I'm designing an arm that can manipulate objects on a table.
My question is about the arrangement of the degrees of freedom.
Different robots seem do have different arrangements of the degrees of freedom,.
e.g. the open-source thor robot uses [yaw-roll-roll-yaw-roll-yaw], while Google's in-house arm uses [yaw-roll-yaw-roll-yaw-roll-roll].
Is there any reason you would choose one specific arrangement over another?
Good Question. The number, arrangement, and orientation of DoFs in the robot should not be taken lightly. It should reflect the robot's desired purpose. Care must be taken to place the "sweet spot" of the arm's workspace in a good place relative to the rest of the robot. And if there will be 2 arms, you probably also want to overlap their workspaces significantly (or not).
N. Staub already mentioned number of DoFs and placement of the (heavy) motors. Physical constraints like this are obviously very important.
The orientation of joints can also drastically affect the robot's workspace. Take a look at these examples:
Lastly, the arrangement of the DoFs can also change the usable workspace of the arm. There are many metrics that can be used to determine the arm's "sweet spot". Manipulability measure is one such metric. Here i some analysis I did on a 5 DoF humanoid arm, (3 DoF shoulder, 1 DoF elbow, 1 DoF wrist). I analyzed 2 different shoulder configurations: Roll-Pitch-Roll, and Yaw-Pitch-Roll. Link lengths are identical, and I think the joint limits are analogous. Color codes denote the scale of the manipulability measure. Red is large, Green is low. Larger (redder) is better. There is an isometric view in the upper left, and 3 orthogonal views. Front view is in the lower right. For the orthogonal views, what is shown is a slice through workspace close to the elbow joint. The robot's torso is gray, upper arm is red, lower arm is green, and wrist is blue. This is the robot's right arm. As shown, the arm is sticking straight out of the torso.
You can see that the shape of the sweet spot is different between the two arms. For Roll-Pitch-Roll it is more up and down. And for Yaw-Pitch-Roll it is more left to right. If the X axis points forward, Y points to the left of the robot, and Z points up, then the best manipulability space for the RPR configuration is like a doughnut around Y axis, and around the Z axis for the YPR configuration.
Lastly, if you are interested in designing robot arms, I highly recommend the book: "Robot Evolution: The Development of Anthrobotics" by Mark E. Rosheim.
One thing you should note is the difference between the number of DoFs. Do you want a robot for a specific task or do you want a versatile robot.
If you want a specific task robot, chance are that you can optimize your DoFs arrangement for the task at hand.
If you want a generic robot then you have way more freedom. From my experience, the choice of DoFs and their arrangements is mostly constrained by the available motors and the wrench you want to exert at the end-effector. Also if the considered motor have angular limits the shape of the workspace is impacted by the arrangement of the DoFs. Lastly the location of the motor influence the inertia of the robot, hence the dynamic motion. For example for very fast motion, like pick and place delta robots are preferred as the motors are fixed to the base when the end-effector moves.
