Download Robot Geometry 1: Determining Manipulator Parameters and Joint Angles and more Exams Mechanical Engineering in PDF only on Docsity! EML 6281 – Robot Geometry 1 Exam 2 – thru Chapter 7 22 Oct 2008 55 minutes, open book and notes You are working with a RCPRP manipulator (the first joint at the base is a revolute joint and the last joint of the manipulator is a prismatic joint). a) What is the mobility of this manipulator? The mobility is equal to the sum of the freedom of the joints. The mobility of this manipulator is 6. b) List all the constant mechanism parameters. The constant mechanism parameters are: a12, a23, a34, a45, α12, α23, α34, α45 S4, θ3 Note that although the fifth joint is a prismatic joint and θ5 will be constant, the value for θ5 is not known until the direction for a56 is chosen (see part c). c) What free choices are made to establish a standard coordinator system on the last moving body of the manipulator? What new parameters are now known? Since the last joint of the manipulator is a prismatic joint, the coordinate system attached to the last moving body will be attached such that the origin lies on the body on the S5 axis. Its Z axis will be parallel to S5 and its X axis will be attached to the body such that it is perpendicular to the direction of S5 . The angle θ5 will now be a known constant. d) You are given a desired position and orientation of the coordinate system attached to the last moving body, i.e. F5T . What free choices do you make so that the hypothetical joint axis S6 is defined? Values for a56 and α56 are selected. Typical values are a56=0 and α56=90. e) What parameters are determined when you “close the loop” in order to form a hypothetical closed loop mechanism? S6, a61, S1, θ6, α61, γ1 f) Explain how you would determine the variable joint angles φ1, θ2, and θ4 that will position and orient the end effector as desired. The figure shows a planar representation of the equivalent spherical mechanism. The angle θ6 is known from the close-the-loop step. The angles θ3 and θ5 are known constant mechanism parameters. 6 5 4 3 2 1 R R R R If you decide to solve for θ2 first the cosine law Z56 = Z32 is used to get an equation of the format Ac2 + Bs2 + D =0. Solving this equation will give two solutions for θ2. Corresponding values for θ1 can be obtained from the two equations X56 = X321 Y56 = - X * 321 . Corresponding values for θ4 can be obtained from the two equations X65 = X234 Y65 = - X * 234 . If you decide to solve for θ1 first the cosine law Z561 = Z3 is used to get an equation of the format Ac1 + Bs1 + D =0. Solving this equation will give two solutions for θ1. Corresponding values for θ2 can be obtained from the two equations X561 = X32 Y561 = - X * 32 . Corresponding values for θ4 can be obtained from the two equations X165 = X34 Y165 = - X * 34 . If you decide to solve for θ4 first the cosine law Z6543 = c12 is used to get an equation of the format Ac4 + Bs4 + D =0. Solving this equation will give two solutions for θ4. Corresponding values for θ2 can be obtained from the two equations X6543 = s12s2 Y6543 = s12c2 . Corresponding values for θ1 can be obtained from the two equations
