Heat oven to 400°F.
In the bowl of an electric mixer combine 1 1�? cups sugar, shortening, eggs, milk and vanilla. Beat at medium speed until well blended.
In a medium bowl combine flour, cream of tartar, baking soda and salt. Add gradually to shortening mixture at low speed. Mix just until blended.
In a small bowl combine remaining 1�? cup sugar and cinnamon. Shape dough into 1-inch balls. Roll in sugar-cinnamon mixture. Place 2-inches apart on ungreased baking sheets.
Bake 7 to 8 minutes. Cool 2 minutes on baking sheets. Place on cooling racks to cool completely.