Example 6 As shown in Figure $6, \odot O$ is the circumcircle of $\triangle A B C$, and point $H$ is the orthocenter of $\triangle A B C$. Let $B C=a, C A=b$, $A B=c$, and the radius of $\odot O$ be $R$. Try to express the length of $O H$ using $a, b, c, R$.

Express the length of $O H$ using $a, b, c, R$.