{"id":558707,"date":"2024-11-05T18:21:47","date_gmt":"2024-11-05T18:21:47","guid":{"rendered":"https:\/\/pdfstandards.shop\/product\/uncategorized\/esdu-860262011\/"},"modified":"2024-11-05T18:21:47","modified_gmt":"2024-11-05T18:21:47","slug":"esdu-860262011","status":"publish","type":"product","link":"https:\/\/pdfstandards.shop\/product\/publishers\/esdu\/esdu-860262011\/","title":{"rendered":"ESDU 86026:2011"},"content":{"rendered":"

INTRODUCTION<\/strong><\/p>\n

This Item presents an introduction to the use of polynomial
\nequations to model the motion of a cam and its follower. The Item
\nforms part of a series (References 1 to 16) that offers guidance on
\nthe design and analysis of cam and follower mechanisms. It is
\nassumed that the user is familiar with other Items in this series
\nand particular reference is made to ESDU 82006[2]<\/sup>,
\nSelection of DRD Cam Laws, and ESDU 83027[6]<\/sup>, ESDU
\n92014[10]<\/sup> and ESDU 93002[12]<\/sup> relating to the
\nblending of cam profiles.<\/p>\n

This Item presents three approaches by which a polynomial can be
\nused to satisfy a set of cam and follower motion requirements.<\/p>\n

For the first approach a minimum-order
\npolynomial<\/strong> is chosen, using successive power terms whose
\nnumber is sufficient to satisfy the prescribed motion requirements.
\nThese will consist of the boundary conditions specifying the start
\nand end of a segment or part of a segment and, possibly, precision
\npoint\u2020<\/sup> conditions within a segment. Such motion
\nconditions may include displacement, velocity, acceleration and
\nother higher derivative values. The order of the polynomial is one
\nless than the number of imposed conditions. The coefficients of the
\nterms of the polynomial are determined from a set of simultaneous
\nequations, equal in number to the number of coefficients. A
\ncomputer program incorporating a routine for the solution of this
\nset of linear simultaneous equations is described in Appendix B and
\nhas been used throughout this Item, when applicable, to obtain
\ndisplacement, velocity, acceleration and jerk equations for the
\nexamples in this Item. Computer input and output files for these
\ncases are also provided.<\/p>\n

A process called exponent manipulation<\/strong> provides
\nthe second approach. As before the number of terms is determined by
\nthe boundary conditions, giving a unique polynomial of higher-order
\nthan the minimum-order equation derived by the use of the first
\nmethod. The result is a non-successive power series, the
\nlower-order terms of the minimum-order polynomial being replaced by
\nan equal number of higher-order terms. The polynomial is still
\nunique but the follower lift in comparison with results from the
\nminimum-order polynomial is more gradual at the start of the rise
\nmotion and more rapid at the motion end. This "skewness" of the
\ndisplacement and higher derivative curves increases with the order
\nof the polynomial and this characteristic may be used to satisfy
\nprecision points.<\/p>\n

Blending<\/strong> provides the third approach. Parts of
\na motion segment satisfied by individual polynomials are coupled to
\nform a complete segment. Blending points are necessarily precision
\npoints in the complete segment. Smooth transition from one
\npart-segment to another requires a common displacement and velocity
\nat each blending point and may also require common accelerations
\nand higher derivatives. A polynomial law part-segment may also be
\nblended with part-segments defined by other cam laws. When blending
\nis used with minimum-order polynomials for parts of a motion
\nsegment, the computer program can be used to obtain polynomial
\nsolutions. Computer input and output files for these examples are
\nprovided.<\/p>\n

Appendix A provides a list of the coefficients and polynomial
\nequations of the standard cam laws used in this Item.<\/p>\n

Comprehensive examples are included in the Item to illustrate
\nand compare the approaches that are presented.<\/p>\n

\u2020<\/sup> In this Item "precision point" is taken to mean a
\npoint on the follower path and\/or a specific follower velocity and
\n\/or acceleration that is to be reached at a specific cam angle
\nwithin that motion segment.<\/p>\n","protected":false},"excerpt":{"rendered":"

Introduction to Polynomial Cam Laws<\/b><\/p>\n\n\n\n\n
Published By<\/td>\nPublication Date<\/td>\nNumber of Pages<\/td>\n<\/tr>\n
ESDU<\/b><\/a><\/td>\n2011-03<\/td>\n73<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n","protected":false},"featured_media":558713,"template":"","meta":{"rank_math_lock_modified_date":false,"ep_exclude_from_search":false},"product_cat":[2675],"product_tag":[],"class_list":{"0":"post-558707","1":"product","2":"type-product","3":"status-publish","4":"has-post-thumbnail","6":"product_cat-esdu","8":"first","9":"instock","10":"sold-individually","11":"shipping-taxable","12":"purchasable","13":"product-type-simple"},"_links":{"self":[{"href":"https:\/\/pdfstandards.shop\/wp-json\/wp\/v2\/product\/558707","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/pdfstandards.shop\/wp-json\/wp\/v2\/product"}],"about":[{"href":"https:\/\/pdfstandards.shop\/wp-json\/wp\/v2\/types\/product"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/pdfstandards.shop\/wp-json\/wp\/v2\/media\/558713"}],"wp:attachment":[{"href":"https:\/\/pdfstandards.shop\/wp-json\/wp\/v2\/media?parent=558707"}],"wp:term":[{"taxonomy":"product_cat","embeddable":true,"href":"https:\/\/pdfstandards.shop\/wp-json\/wp\/v2\/product_cat?post=558707"},{"taxonomy":"product_tag","embeddable":true,"href":"https:\/\/pdfstandards.shop\/wp-json\/wp\/v2\/product_tag?post=558707"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}