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I am having a bit of trouble with the pictured question:

enter image description here

I am able to do part a and b, however c is proving very difficult. My lecturer never really explained much beyond what is asked in a and b. Any hints about how to do it would be greatly appreciated. I have looked at inverse kinematics but that seems to be for determining the angles of the joints, not the length of links and distances.

Thanks in advance for any help!

Paul

Here is the diagram of the robot also:

enter image description here

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  • $\begingroup$ I appreciate that my post is a bit vague but I'm really struggling with it. My understanding is that for part c, my working from a and b is not required, hence why I havent uploaded it. $\endgroup$ – Paul Wilson May 15 '18 at 14:00
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    $\begingroup$ The drawing of the robot would help as the total number of axes is not specified. I also think that the notation is note consistent and will consider $L_i = l_i$ $\endgroup$ – N. Staub May 16 '18 at 7:48
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The question is meant to see if you have learned anything about the underlying math and geometry associated with kinematics rather than just blindly following the basic steps for calculation.

Draw the robot, compare the symbolic version of the calculation with the numerical results listed, and it should be straight forward. Using what you know about figure Q1 will let you simplify the symbolic calc.

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  • $\begingroup$ Yes I've already drawn it and tabulated the D-H parameters for each of the axis. Sorry for being so stupid about this but I'm struggling to see how to do this. $\endgroup$ – Paul Wilson May 15 '18 at 16:05
  • $\begingroup$ Using only variables (the first matrix in C, nothing from the table or other parts of the question) calculate 0T2 and add it to your question. If it's unclear how to do this, reread your text book section about transform matrices. $\endgroup$ – hauptmech May 15 '18 at 22:09
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The question makes you reflects on the meaning of the transform matrix (which construction process w.r.t. DH parameter is given).

A transformation matrix denotes the transformation from one frame to the next, by mean of both a rotation matrix ($R$) of the second frame w.r.t the first frame expressed in the first frame, and a position vector ($p$) of the second frame origin expressed in the first frame.

The transformation matrix is constructed as follows: $T=\begin{bmatrix} R & p \\ 0~0~0 & 1 \end{bmatrix}$

Thenn what I would do, although it is bit unclear from the formulation, I would suspect that the information given relative to the distance between link 2 and 5 (is 5 the end effector?) are given in the base frame (0), otherwise the information relative to $^2_5T$ are not useful. From there using the transformation matrix at hand and considering the suggested vector you get a system of equations.

That gives you relationships between all the mentioned quantities, but there I am blocked by the information concerning the the $y$ component of the position of end-effector w.r.t 2 expressed in 0, as it didn't match my result and left me with $d_5$ unknown (same if I make the assumption that the information about the vector are expressed in 2). Although if the vector component information concerns $x$ than it is possible to get a numerical evaluation of $d_3$.

NOTE: done during my coffee break

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