Assignment #6 - Robot Manipulators | E C E 455, Assignments of Electrical and Electronics Engineering

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ECE 455/655, Fall 2009, Assignment 6 Due: in class, Thursday 11/5/09 1. The two axis (RP) planar polar manipulator in (A) is to be approximated by the two point mass model (B). Gravity is in the direction shown. Note: the point mass assumption in (B) implies zero link inertias, i.e. no rotational kinetic energy terms in K). (a) Show that, given the model (B), the manipulator has kinetic energy (recall sin? a+cos? a=1): — oe {0 consraeT, 262 A “ f K=05(m 70 + m0 +m, F) i or vaRy ' and potential energy ~ Me a P=mgr,sin(@) +m, gr, sin(A) (b) Use the results from (a) and Lagrange’s equations to form the dynamics of this manipulator (using the model (B)). (Generalized force/torque [7,, f, corresponding to joint variables [6,7,].) Write the result in the form t=[D(q)]4+[C(a.4)]4+ g(q). > (A) UA | ¥ j aX \ me ty \ * SSF \Eeo ON 2. Consider the spatial (RR) manipulator shown in (A), which is to be approximated by the (single point-mass) model in (B). Gravity is g in the (-z) direction. @ Y 7 i | ( 2,4 , a