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JohnDTill / ContinuumRobotExamples

An incremental guide to continuum robot mathematical modeling and numerical implementation. The examples are divided into chapters within the folder structure, and each chapter contains a PDF and code examples.
MIT License
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Questions regarding the formulation of the static equation in 01_Statics/02_CSG_Inverse_Kinematics/CSG_Inverse_Kinematics.pdf #16

Closed rodriguesvinay closed 1 year ago

rodriguesvinay commented 1 year ago

the pdf on page.2 says "array 'r' which contains the translation from the end effector to the rod attachment points in the end effector frame" and you used 'r' in the EM summation. Isn't for the EM summation we need p_i(L_i) x n_i instead of R. r_i x n_i in reference frame?

JohnDTill commented 1 year ago

Hi Rodrigues, both versions are correct. The expression sum over i of -p_i(L_i) x n_i - m_i is the sum of moments about the origin. The expression sum over i of -R*r_i x n_i - m_i is the sum of moments about the end effector. In static equilibrium, the sum of moments at any point will be zero, so we are free to pick the point which is most convenient.

rodriguesvinay commented 1 year ago

Hello John, thanks for the explanation. Just curious why it was convenient for you to choose the R. r_i expression?

JohnDTill commented 1 year ago

Probably it was chosen based on the intuition of summing loading on the end-effector at it's centroid, which I find a bit simpler conceptually when formulating the model. However, that does involve an unnecessary rotation which isn't present in the expression you suggest, so I don't really have a preference for one over the other!

rodriguesvinay commented 1 year ago

Hello john, I am sorry I forgot to mention that in formulation of EM, why didn't you considered -pd x F or am I missing somethin?

JohnDTill commented 1 year ago

Right, when considering a force on the end effector, there is an additional term in the sum of moments equation for the force. This additional term reduces to zero when summing moments at the end effector centroid, because the centroid is the point of force application, and the moment arm is zero.

rodriguesvinay commented 1 year ago

Hello john, I was curious if I can contact you through email or something for general conceptual questions instead of opening an issue. I am working on my thesis topic "Kinetostatic analysis of a 6 RUS parallel continuum robot". My email address is **** and you can ping me if it sounds good. Thanks.

JohnDTill commented 1 year ago

Sure thing, I sent you an email