Mechanisms and Dynamics Assignment

Questions: A typical jamb-type tilting garage door opening mechanism is illustrated below: Point G is the centre of mass, and point H is the fixing point for the garage door opener. q is the angle between AC and horizontal, w is the corresponding angular speed. Tasks In this assignment you are required to write a report concerning the planar mechanism in the figure above. In your report, you must: 1. Describe the links and pairs and calculate the mobility. 2. Draw a fully dimensioned drawing of the mechanism shown, making reasonable estimates of all dimensions necessary to define the location of all points A to G. 3. Estimate the mass of the door. You may assume that other mechanism components are massless. 4. Plot the locus of all points from door closed to door open. 5. Write vector equations relating the location of all points as a function of q. 6. Use your equations derived in 5 to plot the x and y position of all points as a function of q. 7. Write vector equations relating the velocity of all points as a function of q for constant w = 1 rad/s. 8. Show velocity vectors, to scale, for all points when the door is fully open, fully closed, q = 0 and q = -30. Assume that w = 1 rad/s and the door is opening in all cases. Answers: The given jamb-type garage door opening mechanism is as follows:The flexibility of a segment is the amount of degrees of opportunity with which it may move. This musing is numerically practically identical to the estimation of the game plan set of the kinematic circle conditions for the framework. It is all around understood that the conventional Grubler-Kutzbach formulas for compactness can't be a good fit for phenomenal classes of parts, and extensively more refined prescriptions considering migration bundles disregard to adequately envision the convenientce of charged "limitless" frameworks. This article discusses how late results from numerical scientific geometry can be associated with the subject of instrument convenientce. In particular, given a social affair configuration of a segment and its circle conditions, an adjacent estimation test places limits on the convenientce of the related party mode. A transparently open programming code makes the idea easy to apply in the kine matics region. Allow n to be the no. of associations in a segment out of which, one is settled, and let j be the no. of clear pivots (i.e., those interface two associations.) Now, as the (n-1) joins move in a plane, with no affiliations, each has 3 level of chance; 2 bearings are required to decide the region of any reference point on the association and 1 to demonstrate the presentation of the association. When we relate the connections there can't be any relative understanding amongst them and one and just encourage is vital to demonstrate their relative introduction. In this way, 2 degrees of chance (elucidation) are lost, and one and just level of adaptability (rotational) is gotten out. Along these lines, no. of degrees of chance is: Most instruments are obliged, ie F=1. In this manner the above connection gets to be, 2j-3n+4=0 This is called Grubler's Criterion. Frustration of Grubler's standard, A higher pair has 2 degrees of adaptability .Following the same dispute as some time as of late, The degrees of chance of an instrument having higher sets can be made as, F=3(n-1)- 2j-h Much of the time a couple of segments have an overabundance level of adaptability. In case an association can move without making any advancement in whatever is left of the instrument, then the association is said to have a dreary level of opportunity. (3). Now estimating the mass of the door to be 50 kg Thus the weight of the door = Mg Thus the weight of the door = 50*9.81 Thus the weight of the door = 490.5 N Now assuming the angle GOD = 300 and for this angle the force required will be (5). The vector equations regarding the location of the points can be written as In the similar way the vector loop equation can be written as This vector equation in Cartesian coordinates can be written as (7). When the angular velocity Writing the velocity vector equations Where a is the location of the points. Then the angle can be calculated as Location would be Therefore the velocity vector for location Therefore the velocity vector for location (8). When the door is fully open When the door is fully closed When The velocity vector for location The velocity vector for location References Belles, D. (1994). Regulating Foam Plastic Insulated Garage Doors: A Summary of Research for The National Association of Garage Door Manufacturers. 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