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The length of the last link (1.73) of my model (of a human finger) is not represented in any of the parameters that I calculated using the Denavit-Hartenberg algorithm, which I think can't be right. I suppose it should be represented in either a₃ or α₃, but those are both 0. It should be noted that the model has no end-effector/tool, but I aligned the z₃ with the approach vector anyway. If anyone has an idea where I'm messing up, that would be much appreciated! The model in question:

Denavit-Hartenberg representation of a human finger

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3 Link Planar robot arm

Note that in your drawing theta_p and theta_d angle are negative according to the right hand rule. That's the first mistake you made, to elaborate, theta_1 is equal to -theta_p.

Also in the last row of your DH table, the translation of DP is in the negative Y direction. Do not forget that the order matters - although there are 5 different combinations of orders of matrix multiplications to calculate the homogeneous transformation matrix.

Forget about the 5 different combinations and stick with the standard one: First rotation about Z Second translation along Z Third translation along X Fourth rotation about X

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I'm not sure why you're not following your own pattern. You have

a1 = PP;
a2 = IP;
a3 = 0;

Why would a3 not be DP?

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  • $\begingroup$ Because it is zero according to the algorithm (Slide 17: cs.uu.nl/docs/vakken/moma/Kinematics_for_Arms.pdf). It has to do with the orientation of the last coordinate frame at the fingertip, but that is the official way of placing it. $\endgroup$ – EmielBoss Oct 20 '17 at 19:41

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