中文摘要：

自由度问题是一个已经持续了150年的热点问题。本文目的在于说明如何用简单方便的公式计算那些高度复杂机构的自由度。本文集中分析了一些公认的比较难的现代并联机构和古典“反常”机构。运用以前所知的公式并不能解出这些机构的自由度。

英文摘要：

The mobility problem is a hot point lasting about 150 year. The objective of this paper is to demonstrate how to use the simple and uniform formula for quickly analyzing the mobilities of those highly complicated mechanisms. The paper focuses on the mobility analyses of the recognized difficult modern parallel manipulators and classical ＂paradoxical mechanisms＂. They are never solved directly by using known formulas before.