Just like the cash register (checkbook) lists bank payments & receipts, a petty cash register is needed to record actual cash transactions for your cash on hand.
This will be a list of all the cash payments detailed in a similar way to the cash disbursements register. The totals are Debited to the individual purchase/expense accounts & Credited to the Petty Cash Control account.
The cash used for these cash payments will come either from the bank or from cash sales. So, there will be a column "Cash from bank" within the cash disbursements register (Dr to the petty cash control account). Cash sales are Credited to the sales account & Debited to the petty cash control account.