This paper focuses on the method of solving the non-linear equation arising form the synthesis of plane rigid guidance. Based on the concept of universal Grey number and the rules of four algebraic operation of universal Grey number

it is introduced that universal Grey number is changed into interval Grey number

then gives interval analysis with extensible characteristic of universal Grey number. According to the characteristic of universal Grey function

namely

if there has solution in the universal Grey interval

it must be 0∈F（X）

confirming whether it has solution and removing non-solution interval and decomposing interval that has some solutions

finally finding all solutions of non-linear equation. Universal Grey function can deal with some problems that Grey number or interval analysis can’t. Based on the characteristic of universal Grey function

a new method has been proposed. At last an example is given.