MechMa2 The progression of the MechMaX group exercises can be described by: Initial design -> perform kinematic analysis -> Introduce Dynamics -> improve the mechanism performance through synthesis -> Validation of performance -> balancing -> continued validation and uncertainty quantification. 1. Parameterize your simulation model in preparation for dynamics and synthesis. By this we mean two things: a. Place your body reference frames in the centroid. As you don’t know yet where your centroid is going to be (you have not made the final design yet), it might be a good idea to make a “design” reference frame like how you defined the body reference frame for kinematic analysis in MechMa1 and locate the centroidal fixed reference in the body-fixed design frame. We describe the internal orientation from ’- frame to ’’-frame using the C orientation matrix. C is a constant matrix as it relates the orientation of two reference frames in the same rigid body. You could use the same orientation for the centroidal body-fixed reference frame as your design frame if it makes sense from a geometrical point of view of the body at hand (does the alignment makes sense according to the dominant features of the geometry). b. Parameterize the location of the body CG, using 𝑟𝑟 ′′𝐶𝐶𝐶𝐶 , the joints and Point Of Interest (POI) using 𝑠𝑠′ 𝑃𝑃 = �𝑠𝑠′ 𝑥𝑥 𝑃𝑃 𝑠𝑠′ 𝑦𝑦 𝑃𝑃 � in the centroidal fixed reference frame using the location vector of the centroidal based origo as illustrated in the figure at the bottom by introducing the ’’ design frame. Remember that for dynamic analysis your generalized coordinates are the location of the centroidal fixed reference frame and the orientation for all bodies. 2. Perform posture analysis (Newton-Raphson) and generate the trace (path) of the Point Of Interest (POI) as you defined in MechMa1 by plotting its coordinates and the orientation of the host reference frame as a function of time. Validate that your results using centroidal fixed reference frame are the same as you got from MechMa1. (You can do this by overlaying the traces of the POI from MechMa1 with that of MechMa2, or plot the difference between the x and y coordinates of the POI using centroidal fixed reference frame and what you did in MechMa1. Similar, also show that the global orientation is the same. (You might have to consider the constant relative angle between centroidal reference frame and the design reference frame in case they are not aligned). 3. Determine the global velocity and acceleration of the POI as well. (Remember those are the linear equations)