Question

When is the president of the Senate allowed to vote on legislative matters? to end debate on the floor to bring bills to the floor for debate to register the position of the executive branch to break a tie vote on a bill

Answer 1

Answer; 
To break a tie vote on a bill
 
The president of the Senate is allowed to vote on legislative matters in order to break a tie vote on a bill. 

Explanation;
Under Article I, section 3 of the constitution, The vice president of the United states shall be the president of the state, but shall have no vote; unless they be equally divided.
The president of the senate presides over the senate only on ceremonial occasions or when a tie-breaking vote may be needed. 

Answer 2

The president of the Senate is allowed to vote on legislative matters only to break a tie vote on a bill. This situation is quite rare in the Senate, which contains majorities and minorities.