# Precision Design Case Studies

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Study Paper: Precision Design Submitted by: Yan Pui Isabel TAI (Student ID: 20189187) Class: MECH4720 Introduction to Precision Engineering Date of Submission: May 22, 2016 Course Instructor: Professor Yongsheng GAO Department of Mechanical and Aerospace Engineering Hong Kong University of Science and Technology Clear Water Bay, Kowloon Hong Kong 1. Selected design The suitable assembly system for this study is the linkage as shown in Figure 1. Four hinged bars are consisted in the system. The end points of the bar are indicated as point A to E. There are five bar segments in this system where bar AC is assumed to be parallel to the ground, also known as the datum of the structure. Bar BE and CD are hinged together…show more content…
_x _=[_(_a@_b@_(_(_c@_d)@_(_____a@_____b )))] n+n+m+1-q=6 _u _=[_(___c@___d@___dx )] m+q=3 __H__x=[cos____a _,cos_(__a-__b ),cos_(__a-__b-__c ),cos_(__a-__b-__c-__d ),-a sin____a _-b sin_(__a-__b )-c sin_(__a-__b-__c )-d sin_(__a-__b-__c-__d ),-b sin_(__a-__b )-c sin__(__a-__b-__c )-d sin_(__a-__b-__c-__d ) _ ]_x _+[c sin__(__a-__b-__c )+d sin_(__a-__b-__c-__d ) _,d sin_(__a-__b-__c-__d ),0]_u _ __H__y=[sin____a _,sin_(__a-__b ),sin_(__a-__b-__c ),sin_(__a-__b-__c-__d ),a cos____a _+b cos_(__a-__b )+c cos_(__a-__b-__c )+d cos_(__a-__b-__c-__d ),b cos_(__a-__b )+c cos_(__a-__b-__c )+d cos_(__a-__b-__c-__d ) ]_x _+[-c cos_(__a-__b-__c )-d cos_(__a-__b-__c-__d ),-d cos_(__a-__b-__c-__d ),0] _u _ __H___=[0,0,0,0,1,-1]_x _+[-1,-1,1]_u _ _H=[_(__H__x@__H__y@__H___ )]^ Substitute the nominal value into the equation: _H=[_(_(-1&0&1.00@0&1&0.45@0&0&0)&_(0.46&0&0@-0.89&0&0@0&1&-1))]_x _+[_(0&-88.56&0@53.31&0&0@-1&-1&1)]_u _=A_x _+B_u _ Therefore, A=[_(_(-1&0&1.00@0&1&0.45@0&0&0)&_(0.46&0&0@-0.89&0&0@0&1&-1))] B=[_(0&-88.56&0@53.31&0&0@-1&-1&1)] Since the vector chain is closed, _u _=-B^(-1) A_x…show more content…
The ratio of the improvement in precision to the increase in cost percentage is much higher in case II. This implies smaller cost increment can achieve a higher precision improvement. 5 Recommendation on choice of approach when upgrading product quality _ Based on the analysis, case II is a more economical choice as smaller cost addition can lead to a more improvement of precision in the assembly. As a company which aims to upgrade the product quality, cost is the major concern for choosing an appropriate method. Hence, case II is the suitable approach. To optimize the cost effectiveness of the method for improving precision of components, further analysis can be done. Improving the precision of two or more components may attain better and more economical results. 6. References  Gao, Y., 2016, “Introduction to Precision Engineering”, Lecture Notes, HKUST, Hong Kong.  Zhang, H.C., 1997, “Advanced Tolerancing Techniques”, John Wiley and Sons, New