Planetary gear train of automatic transmission for vehicle

A planetary gear train of an automatic transmission for a vehicle, the planetary gear train comprising:

• a first planetary gear set having first, second, and third rotational elements;
• a second planetary gear set having fourth, fifth, and sixth rotational elements;
• a third planetary gear set having seventh, eighth, and ninth rotational elements;
• a fourth planetary gear set having tenth, eleventh, and twelfth rotational elements;
• a first external gear set having thirteenth and fourteenth rotational elements;
• a second external gear set having fifteenth and sixteenth rotational elements;
• an input shaft coaxially arranged with the first, second, and third planetary gear sets and the thirteenth and fifteenth rotational elements;
• and
• an output shaft arranged in parallel with the input shaft and coaxial with the fourth planetary gear set and the fourteenth and sixteenth rotational elements,
• wherein the first rotational element is fixedly connected with the fourth rotational element, and selectively connected with a transmission housing,
• the second rotational element is fixedly connected with the input shaft,
• the fifth rotational element is fixedly connected with the fifteenth rotational element,
• the sixth rotational element is selectively connected with the transmission housing,
• the seventh rotational element is fixedly connected with the thirteenth rotational element, and selectively connected with the second rotational element and the third rotational element respectively,
• the tenth rotational element is fixedly connected with the fourteenth rotational element,
• the eleventh rotational element is fixedly connected with the output shaft, and
• the twelfth rotational element is fixedly connected with the sixteenth rotational element.