{"id":23440,"date":"2026-02-06T08:00:49","date_gmt":"2026-02-06T13:00:49","guid":{"rendered":"https:\/\/www.purdue.edu\/freeform\/me274\/?p=23440"},"modified":"2026-04-22T16:30:17","modified_gmt":"2026-04-22T20:30:17","slug":"homework-h3-b-sp-26","status":"publish","type":"post","link":"https:\/\/www.purdue.edu\/freeform\/me274\/2026\/02\/06\/homework-h3-b-sp-26\/","title":{"rendered":"Homework H3.B – Sp 26"},"content":{"rendered":"\n\n\n
Problem statement<\/strong><\/em><\/span><\/a>
\nSolution video<\/a>
\n<\/strong><\/em><\/span><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n
\n

DISCUSSION THREAD<\/span><\/strong><\/em><\/p>\n

\"\"<\/p>\n

Any questions?? Please ask\/answer questions regarding this homework problem through the “Leave a Comment” link above.<\/p>\n

\n

Discussion<\/strong><\/em><\/p>\n

<\/p>\n

An animation from the simulation of the motion of the robotic arm system is shown above for a fixed observer. The motion of end-effector B is quite complicated, as can be seen. However, if we attach an observer to section AD of the end link of the arm, the observed motion of B is greatly simplified. In fact, the observer simply sees a back-and-forth motion of B in the x-direction, as shown in the animation below.<\/p>\n

<\/p>\n

HINTS<\/strong><\/em>: The velocity of point B can be found from the following moving reference frame velocity equation:<\/p>\n

v<\/strong><\/em>B<\/sub> = v<\/strong><\/em>A<\/sub> + (v<\/strong><\/em>B\/A<\/sub>)rel<\/sub> + \u03c9<\/strong><\/em> \u00d7 r<\/strong><\/em>B\/A<\/sub><\/p>\n

With the observer on link AD, we know the following:
\nvA<\/sub> = <\/strong>(L \u03b8_dot) i<\/strong><\/em>
\n\u03c9<\/strong><\/em>\u00a0 = \u03c6<\/em>_dot k<\/strong><\/em>
\n(v<\/strong><\/em>B\/A<\/sub>)rel<\/sub> = b<\/em>_dot i<\/strong><\/em><\/p>\n

Use similar logic for writing down the acceleration of B. Be careful in writing down the expression for\u00a0a<\/strong><\/em>A <\/sub>; in particular, a<\/strong><\/em>A\u00a0<\/sub>\u2260 0. <\/strong>(A is traveling on a circular path with a constant speed.)<\/p>\n

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 <\/p>\n<\/div>\n","protected":false},"excerpt":{"rendered":"

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